# Tagged Questions

This tag is used if a reference is needed in a paper or textbook on a specific result.

**2**

votes

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115 views

### Equivalence of different cohomology groups

Let $X$ be a topological space (may be assumed to be locally compact). Let $A$ be either a field or $\mathbb{Z}$. One can consider various cohomology groups:
(1) singular cohomology ...

**2**

votes

**0**answers

33 views

### Two notions of bundle of C* algebras

One can find in the literature two notions of $C^*$-algebra over a topological space $X$.
The first is as the data of an open surjection $ \pi: B \rightarrow X$ together with the structure of a ...

**8**

votes

**2**answers

253 views

### References for Yang-Mills Theory

We are looking to run a working seminar about the Yang-Mills story. We hope that our seminars is of interest to analysts (working with curvatures and Ricci flows on Riemannian manifolds), the ...

**-1**

votes

**0**answers

34 views

### conformal measures - definitions, examples and references

I would like to know the exact definition of conformal measure in compact and non compact spaces and not compact, as well as examples of conformal measures
Also, if someone can refer me to literature ...

**7**

votes

**1**answer

233 views

### Unique factorization of posets

Given two finite posets $P$ and $Q$, we can form the direct product poset $P \times Q$ whose elements are pairs $(p,q) \in P \times Q$ with $(p,q) \leq (p',q')$ if $p \leq p'$ and $q \leq q'$. Let us ...

**2**

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**0**answers

37 views

### Fracturing $t$-structures

$\def\tee{\mathfrak{t}}$ Let $\tee_1,\tee_2$ be two $t$-structures on a triangulated category $\cal T$; call them fracturing if the two fiber sequences $\tau^\le_1X\to X\to \tau^\ge_1X$ and ...

**1**

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31 views

### explicit conformal map of sinus-shaped region

I wonder weather an explicit conformal map of a sinus-shaped region given by $\Re(z) \in [0, 1+\delta \sin(\Im(z)) ]$ onto say a strip or a ball is known (of course $0<\delta < 1$). Thank you.

**1**

vote

**1**answer

238 views

### Automorphisms of rings fixing all prime ideals

Let $f,g:A \to B$ be two ring homomorphisms of noetherian rings satisfying that for any prime ideal $\mathfrak{q} \subset B$, $f^{-1}(\mathfrak{q})=g^{-1}(\mathfrak{q})=:\mathfrak{p}$ and the induced ...

**1**

vote

**0**answers

52 views

### Need a reference/proof for computing the regularity of ideal of points in $\mathbb P^d$?

In a lecture notes on 'Cohomology modules' i read the following remark:
Given a set $X$ of points in $\mathbb P^d$,using the Local Cohomology modules one can easily compute the reg$(S_X)$ where ...

**1**

vote

**1**answer

64 views

### Reference for a local density theorem for binary vectors

I have the following theorem written on my whiteboard, but have misplaced the reference. I believe the probabilistic method may be involved in the proof. Any pointers appreciated.
Theorem Let ...

**-2**

votes

**0**answers

128 views

### Reference for algebraic manipulation of sheaves [on hold]

I am currently playing with sheaves over families of algebraic varieties ($O_x$-modules) their torsion sub-sheaf, higher direct images and tensor products, I am looking for a good reference to learn ...

**2**

votes

**0**answers

33 views

### Lyapunov exponents of Lorenz63 and Lorenz96 system

Can someone suggest a reference on the mathematical results (NOT numerical) on the Lyapunov exponents of Lorenz-63 and Lorenz-96 systems (or any other non-trivial system)? In particular, is it always ...

**4**

votes

**2**answers

264 views

### Embedding property of weakly compact cardinals

One of the characterizations of $\kappa$ being a weakly compact cardinal is being inaccessible, and for every $\kappa$-model $M$, there is a [$\kappa$-model] $N$ and an elementary embedding $j\colon ...

**5**

votes

**1**answer

68 views

### smoothing locally-finite (Borel-Moore chains)

Let $M$ be a smooth manifold. As is recorded in (for example) Lee's book, de Rham proved that one can calculated singular homology, $H_*(M)$ using smooth simplices. Does the result extend to ...

**3**

votes

**1**answer

203 views

### Euler characteristic - reference question

Let $X$ be an algebraic variety over $\mathbb C$ and let $\mathcal F$ be a constructible sheaf on $X$. It is well-known that the Euler characteristic of the cohomology of $\mathcal F$ is equal to the ...

**0**

votes

**0**answers

64 views

### maximal sets of vertices that avoids a clique

I am looking for some known algorithm that finds, for a given graph, all the maximal sets of vertices that avoid a clique of some given size $k$. I'd prefer one written in MATLAB, but other languages ...

**3**

votes

**1**answer

164 views

### Fréchet L-Spaces

According to the paper The emergence of open sets, closed sets, and limit points
in analysis and topology famous mathematician Maurice Fréchet who introduced the concept of metric spaces has also ...

**1**

vote

**1**answer

150 views

### General Reference for surface singularities

Is there any "standard" reference for (rational) singularities on algebraic surfaces? I'm aware of Artin's papers and the one of Brieskorn (Rationale Singularitäten komplexer Flächen), but they seem ...

**6**

votes

**1**answer

217 views

### “structure group” for fibration

Regarding "fibration" as a homotopy analogue of "fiber bundle",I want to see parallel notions of "structure group" and "fiber change" in "fibration".
Does it make sense to talk about "structure ...

**1**

vote

**0**answers

73 views

### Rank diagrams of permutations $w \in S_{m}$ in the study of complete flag varieties [on hold]

I'm looking for some good references that may either prove or help to prove the following statement: Show that a matrix $r=(r_{pq})_{1 \leq p,q \leq m}$ defines a rank diagram for some pair of ...

**4**

votes

**1**answer

165 views

### exact definition of Fiedler vector

For a given N-vertex similarity graph $ G=(V,A) $ the eigenvalues of the unrenormalized (graph) Laplacian may be denoted as
$$ 0= \mu_0 \leq \mu_1 \leq ... \leq \mu_N $$
where the corresponding ...

**2**

votes

**2**answers

253 views

### Irreducible algebraic sets via irreducible polynomials

There are many results about irreducible polynomials over finite fields:
we know a cardinality of all irreducible polynomials with given degree, we know explicit examples of irreducible polynomials, ...

**2**

votes

**1**answer

134 views

### Small object argument for multiple factorization systems

Is there something similar to the small object argument, but related to a chain of factorization systems on a category $\cal C$?
It is easy to see that one can give a chain of "generating morphisms" ...

**0**

votes

**0**answers

47 views

### “Downward closed” relation on a poset

I say that a relation $R$ on a poset $P$ is downward closed if for each $(x,y)\in R$, and $x'\le x$, then $(x',y)\in R$.
Is there a reference where this thing is studied, maybe under a different name?
...

**3**

votes

**2**answers

245 views

### Applications of space filling curves

I am seeking articles where a space filling curve has been used as a theoretical application, such as in the study of general orthogonal polynomials.

**3**

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**0**answers

30 views

### covariant derivative of manifold-valued function and logarithm map

Let $M$ be a Riemannian manifold and $f\colon \Omega\subset \mathbb{R}^d\rightarrow M$ a smooth, i.e. $C^\infty$, function. For any $p\in M$ let $T_pM$ be the tangent space at $p$ and $\log_p\colon ...

**3**

votes

**0**answers

50 views

### Characteristically simple locally compact abelian groups

Say a topological group $G$ is topologically characteristically simple if there does not exist a closed subgroup $1 < K < G$ such that $K$ is invariant under all automorphisms of $G$ (here ...

**3**

votes

**1**answer

149 views

### discrete Grothendieck construction

In "BASIC CONCEPTS OF ENRICHED CATEGORY THEORY", (version Reprints in Theory and Applications of Categories, No. 10, 2005), chapter 4.7 p.75-76, Kelly introduces the "discrete Grothendieck ...

**0**

votes

**2**answers

270 views

### The Zeta Function Before Riemann [duplicate]

Leonhard Euler studied the function that is now known as the Riemann zeta function. I have not found the notation $\zeta$ in any of the works of any mathematicians prior to Bernhard Riemann's paper On ...

**0**

votes

**1**answer

71 views

### The pointwise Lipschitz-ness of a function on a dense set, implies its pointwise Lipschitz-ness everywhere?

Some definitions: Let $(M,d)$, $(M',d')$ be metric spaces. For $f:M\to M'$, $x\in M$ and $r>0$, define $$D_r(f)(x):= \sup\{r^{-1}d'(f(x),f(y)): y\in M,\,d(x,y)\leq r\}.$$ Define the pointwise ...

**2**

votes

**1**answer

126 views

### Are braid groups conjugacy separable?

I would like to re-ask a question that was raised in the comments here:
Normal subgroups of braid groups
Namely, a group $G$ is called conjugacy separable, if it holds that for every two elements ...

**4**

votes

**2**answers

209 views

### Error estimate in the spectral theorem of compact operators on a Hilbert space

Given a compact self-adjoint operator $K$ mapping $L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d)$ as $f \rightarrow \int K(x,y) f(y) d\mu(y)$, let us define its eigenvalues $\lambda_i$ and ...

**2**

votes

**1**answer

78 views

### About eigen-functions of the Gaussian kernel

If I look at the Guassian kernel function $e^{- \frac {\vert x - y\vert_2^2 }{2 w^2 } }$ for $x, y \in \mathbb{R}$. Then w.r.t the Gaussian measure $N(\mu,\sigma)$ I believe it is true that this has a ...

**3**

votes

**1**answer

117 views

### Decreasing the binding number of an open book while increasing the genus of the pages

Let $(B,\pi)$ be an open book decomposition of a closed, connected, oriented 3-manifold $M$ with odd (even) binding number and with pages of Euler characteristic $\chi$. Is it possible to define ...

**1**

vote

**1**answer

97 views

### What are the best known bounds on the Hermite polynomials?

The best I could find on the net is this paper,
http://arxiv.org/pdf/math/0401310.pdf
Has this been improved?

**6**

votes

**2**answers

205 views

### The Thom space of a Whitney sum of vector bundles

Let $\xi$ and $\eta$ be vector bundles over the same base space $X$. Their Whitney sum is a bundle $\xi\oplus\eta$ over $X$. I read somewhere (without proof) that its Thom space is given by
$$
...

**3**

votes

**0**answers

175 views

### An explicit formula for $\zeta(2m+1)$ with good convergence

The question: Is the following formula known?
$$\zeta(2m+1)=\frac{(-1)^m 2^{4m+2}\pi^{2m}}{2^{2m}-1} \sum\limits_{k=1}^m \frac{(2^{2k}-1)b_{2k}}{2^{2k}(2k)!} \sum\limits_{v=k}^m ...

**2**

votes

**0**answers

46 views

### Good reference for noncommutative Lp spaces

I'm looking for good references to learn about Lp spaces associated with von Neumann algebras. I already know about Uffe Haagerup's paper "Lp-spaces associated with an arbitrary von Neumann algebra"; ...

**15**

votes

**4**answers

1k views

### Languages beyond enumerable

A language is a set of finite-length strings from some finite alphabet $\Sigma$.
It is no loss of generality (for my purposes) to take $\Sigma=\{0,1\}$; so a language is a set of bit-strings.
...

**1**

vote

**1**answer

403 views

+50

### A paper by Y. Morita

The corresponding bibliographical details are:
Yoshihito Morita, Elementary proofs of the commutativity of rings satisfying $x^{n}=x$. Mem. Defense Acad. 18 (1978), no. 1, 1–24.
Does anybody here ...

**2**

votes

**0**answers

64 views

### reference for KK theory

I wanted to ask you, if you have any good references (book or pdf) to learn about the KK theroy of Kasparov. I think the presentation of Blackadar is too close from the commutative theory.
I was ...

**16**

votes

**0**answers

238 views

+500

### Is this a model for $K$-theory of a triangulated category?

The recent question Complete the following sequence: point, triangle, octahedron, . . . in a dg-category reminded me of something I wanted to clarify long time ago; most likely this is now well known ...

**0**

votes

**1**answer

90 views

### Graph Isomorphism for Triangle Free graph

Is there any specific computational complexity result of Graph Isomorphism for Triangle Free graphs?
Anything close to the subject will help and of course, I have searched Google.

**2**

votes

**0**answers

36 views

### Estimates for hyperbolic metrics on nested surfaces

Suppose that $X$ and $Y$ are connected hyperbolic Riemann surfaces, with $X\subsetneq Y$. Let $\rho_{X,Y}$ be the density of the hyperbolic metric of $X$ with respect to that of $Y$; then $\rho_{X,Y} ...

**3**

votes

**0**answers

104 views

### “Parameterising” extensions $0\to E\to W\to F\to 0$ by $\mathbb P(H^1(E\otimes F^*))$?

Let $X$ be a complex projective manifold and $E$ and $F$ be holomorphic vector bundles on $X$. The extensions of $F$ by $E$ are classified by elements $e\in H^1(E\otimes F^*)$. On the other hand, for ...

**3**

votes

**0**answers

67 views

### Can one push a path out of an algebraic set with control on length?

Consider a real algebraic set $A\subseteq\mathbb{R}^n$. The case I am interested in is a homogeneous cone (i.e., if $x\in A$ then also $\lambda x\in A$ for each scalar $\lambda>0$) where each ...

**3**

votes

**1**answer

74 views

### Functional equations associated with addition theorems for elliptic functions

I'm trying to read the article "Functional equations associated with addition theorems for elliptic functions and two-valued algebraic groups" by Bukhshtaber,V. M. Russian Mathematical ...

**4**

votes

**1**answer

65 views

### Operator space structures on CB(H,K) where H and K are Hilbertian operator spaces?

(I'd be grateful if anyone thinking of putting MathJax in the question title refrains from doing so.)
By consulting various standard sources (Effros-Ruan's book, Pisier's book, the lexicon of ...

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vote

**0**answers

69 views

### A family of rank two bundles on $\mathbb CP^1$ parameterized by $H^1(O(-2n))$

Let $n$ be a positive integer. Consider the family of extensions
$$0\to O(-n)\to E\to O(n)\to 0,$$
parameterized by $H^1(O(-2n))$. For each element $e\in H^1(O(-2n))$ we get a rank two bundle $E$ ...

**1**

vote

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28 views

### What are the central points of a semi-nice region in the plane?

For a convex set in Euclidean space, there is an obvious notion of its center: namely, its center of mass, which by convexity lies in the set. For a nonconvex set there is just as obviously no nice ...