All Questions
8,725 questions
3
votes
0
answers
341
views
Descent of singular cohomology
When proving that singular cohomology of an appropriate space $X$ equals sheaf cohomology of $X$ with "values" (does one say that?) in the sheaf $\mathbb{Z}_X$ of locally constant functions, the ...
- 319
1
vote
0
answers
46
views
spherical map of fixed points?
Let $B = \{\, x \in \Re^m : \|x\| \le 2 \,\}$, and let $f : B \to B$ be a continuous function whose set of fixed points is $S^k = \{\, x \in B : \|x\| = 1, x_{k+2} = \cdots = x_m = 0 \,\}$. Can it ...
6
votes
0
answers
226
views
Joins and classifying spaces in the category of compactly generated spaces
In Milnor's Construction of Universal Bundles, II, he defines $E_nG$ by repeated
joins of $G$ with itself, but he has to use the `strong topology' on the join instead
of the everyday topology that ...
- 12.5k
4
votes
0
answers
317
views
(Equivariant) Sheaves of Equivariant Spectra?
This is a very naive question but 1)given a compact Lie group G, is there a good notion of a sheaf of equivariant spectra on a G-space X analogous to the model structure that Brown develops in his ...
- 3,758
8
votes
0
answers
205
views
Characteristic classes from moduli of alternating forms
Suppose, just for example, that you have a smooth manifold $M$ of dimension greater than $8$,and a cohomology class $q$ in $H^3(M,{\Bbb R})$. Suppose further that one can represent $q$ with a ...
- 17.6k
1
vote
1
answer
256
views
N_3 and N_4 periodic and pseudo Anosov auto-homeomorphisms
It is well know that the genus three non orientable surface, N3, has only periodic and reducible auto-homeomorphisms, meanwhile the surface N4 is the first non orientable surface with pseudo Anosov ...
- 345
2
votes
0
answers
243
views
topology of infinite union of hyperplanes
Hi all:
I am working on Functional Analysis. I encounter a topology problem in my study of spectrum of certain operators, and it has bothered me for quite some time. Any idea or references is greatly ...
- 89
2
votes
0
answers
57
views
Complete rings and modules(topologically)
In the a-adic topology, if M,N are A-modules, and N is the homomorphic image of M, can we prove that N is complete whenever M is? in other words, does completeness carries over to homomorphic images.
- 53
3
votes
1
answer
225
views
Explicit classifying spaces for crossed complexes
I'm trying to understand the topology behind a certain group which fits into a truncated crossed complex, so I've been trying to understand Brown's construction of the classifying space of a crossed ...
- 1,422
3
votes
0
answers
207
views
Symmetric monoidal structure on cosimplicial spaces
Is there a monoidal structure on the category $Spc^{\Delta}$ of cosimplicial spaces such that in the adjunction
$$
\Delta^{\bullet}\otimes-\colon Spc\leftrightarrows Spc^{\Delta}\colon Tot(-)
$$
the ...
- 101
3
votes
1
answer
166
views
Upper bound on the genus of a k-page graph
Is there an upper bound on the genus of a graph that has a book embedding on say k pages, or can the genus be arbitrarily large? If not a general bound is known, what happens for k=3?
- 75
0
votes
0
answers
86
views
Ways to decompose a torus for finite element method so that each cell contains a complete revolution of the major radius
I've got a finite element problem involving paths around the interior of a torus. For this particular problem I think I could make things more computationally efficient if each cell in the mesh made ...
- 101
1
vote
1
answer
231
views
blowing up the graphs
I heard the phrase from many mathematician using in the colloquials. I heard algebraic geometer using it. I was never bother about it until one of my professor responded to one my question as follows:
...
- 121
2
votes
0
answers
270
views
Homotopy equivalences and cores
Hi all,
Before asking my question, I need to fix some terms and notation.
Let $M$, $M'$ be locally compact, Hausdorff spaces, and $f:M\rightarrow M'$ a homotopy equivalence with homotopy inverse $g:...
- 93
2
votes
0
answers
147
views
System dynamic of space euclidean and hyperbolic tilings
Theorem 2.9. (Rudolph [Rud89]) Suppose $X_{T}$ is a finite local complexity (FLC)
tiling space. Then $X_{T}$ is compact in the tiling metric d. Moreover, the action $T$ of
$R^{d}$ by translation is on ...
- 21
5
votes
0
answers
181
views
Are $n$-vector bundles an $(\infty,n)$-symmetric monoidal category with duals?
In Lurie's On the Classification of Topological Field Theories, one of the main characters are $(\infty,n)$-symmetric monoidal category with duals. A basic example of this should be $n$-vector spaces, ...
- 6,777
0
votes
0
answers
82
views
Degree of sequence of mappings
If $f_n$ is a sequence of smooth orientation preserning mappings of degree one between open annuli $A(1,r):=\{x: 1< |x| < r \}$ and $A(1,r_n)$, $r>1$ and $r_n>1$, on the Euclidean space $\...
- 95
5
votes
0
answers
203
views
Homotopy group of space of gauge fields modulo gauge equivalence on T^4
Singer observed in 1978 (Comm.Math.Phys. 60, 7-12) that the homotopy group of the space of gauge fields modulo gauge equivalence with gauge group $G$ on $S^4$ is given by
$\pi_n({\cal A}/{\cal G}) = \...
- 362
3
votes
0
answers
168
views
Mapping into Hurewicz cofibrations.
In Strøm's paper "The Homotopy Category is a Homotopy Category" he proves
(Lemma 4) that if $Y$ is compact and if $i:A\to X$ is a cofibration, then the induced map
$$
i_*: A^Y \to X^Y
$$
is also a ...
- 12.5k
2
votes
0
answers
148
views
Is the homotopy of a primitively generated Hopf algebra still primitively generated?
Let $A=\oplus A_n$ be a primitively generated graded Hopf algebra, where each $A_n$ is a simplicial group. This allows us to define the homotopy group $\pi_*(A)$.
Question: is the graded Hopf algebra ...
- 681
0
votes
0
answers
142
views
Homomorphism between the set of n-flats in $R^m$ to some manifold
I am unaware of what the formal definition of "limit" is for a sequence of flats, but for the purpose of this question her is the definition of limit that I am using:
Consider a sequence $s_1, s_2, ...
- 435
1
vote
0
answers
99
views
n-reduced Eilenberg subcomplex
It is somewhat of a standard construction, that, given a simplicial set K, we can form $E_n K$, by choosing a basepoint, and picking all simplices that map their $(n-1)$-skeleton to the basepoint. If ...
- 41
1
vote
1
answer
170
views
Does there exists a (possibly homological) characterization of the Jordan curve property in all dimensions?
More precisely, let $M$ be a subspace $\mathbb R^n$ with the following properties:
$M$ is a topological manifold of dimension $n-1$.
M is compact.
Does there exist a homological characterization of ...
- 3,699
3
votes
0
answers
189
views
Which local homeos to numerical space are bijective?
I am reading T. Szamuely's book on Galois groups and fundamental groups.
As preparation to the algebraic case, he recalls the topological case.
So I am wondering if a surjective local homeomorphism $f$...
- 211
1
vote
0
answers
79
views
Subresultants of primitive polynomials
Given two primitive polynomials $f,g\in D[x]$ over some domain $D$, is there anything we can say about the primitiveness of their $i$-th subresultant polynomials $Sres_i(f,g)$? I.e. is there a simple ...
