All Questions
9,056 questions
4
votes
0
answers
140
views
Cartesian and strictly associative Path Object.
Let $X$ be a topological space. Is there a path object functor $\mathrm{P}:\mathbf{Top}\rightarrow \mathbf{Top}$, with fibration $ev_{0},ev_{1}: \mathrm{P}(X)\rightarrow X\times X$ such that:
(1) $\...
- 1,974
2
votes
1
answer
190
views
bundle over a chain
Consider the universal bundle $G\hookrightarrow EG\rightarrow BG$. Is it possible to get another bundle $EG|_{B}$ by restricting $EG$ over a smooth singular $k$-chain $B
\in H_k(BG)$ ($k\leq n$)? I ...
- 1,709
1
vote
0
answers
101
views
How can one compute the cohomology of $i'^*C$, for $i':\mathbb{A}^{N-1}\setminus \{0\}\to \mathbb{A}^{N}\setminus \{0\} $?
For an (etale or 'topological', constructible bounded) complex of sheaves $C$ on $X'=\mathbb{A}^{N}\setminus \{0\} $, $i'$ being the embedding $\mathbb{A}^{N-1}\setminus \{0\}\to \mathbb{A}^{N}\...
- 16.9k
8
votes
0
answers
438
views
Differential K-theory computation
I am trying to read about K-theory and differential K-theory. I understand that the K-theory of spheres can be computed explicitly (by getting to the stable range and using Bott periodicity and so on)....
- 3,383
6
votes
0
answers
532
views
Can one calculate Ext's between microlocalized perverse sheaves/D-modules using topology?
So, I know one really good technique for calculating Ext's between perverse sheaves/D-modules using topology: the convolution algebra formalism, worked out in great detail in the book of Chriss and ...
- 44.7k
3
votes
0
answers
251
views
Is an element of the cohomotopy space trivial?
Let as have a continuous map from a topological space X to an n-sphere, realized as a simplicial map between simplicial complexes (for example), i.e. represented by a finite set of data. Is there an ...
- 972
0
votes
2
answers
356
views
Can all induced maps be described categorically.?. (or at least as generally as possible)
Hi: I am new here. I went over the fAQ's, still, sorry if I break protocol.
I am pretty confused about induced maps in different areas of algebraic
topology; I do know how these induced maps are ...
- 1
0
votes
0
answers
185
views
the boundary homomorphism $[\Sigma S^{n-1},X]\to[S^n,X]$ is identity?
Given a Puppe sequence $\cdots \to S^{n-1} \to Y \to S^n(\simeq Y/S^{n-1}) \to \Sigma S^{n-1} \to \cdots$, where $Y=S^{n-1}\cup_{2\iota} e^n$ where $\iota:S^{n-1}\to S^{n-1}$ is identity,
we have a ...
- 699
3
votes
0
answers
122
views
Torsion of Bass, Farrell and Waldhausen nil groups
Let H be an infinite virtually cyclic group. If H is orientable (resp. non-orientable) the Farrell nil groups $N_n(\mathbb{Z}H,\alpha) $ (resp. the Waldhausen nil groups $N^W_n(\mathbb{Z}H;\mathbb{Z}[...
- 235
4
votes
0
answers
208
views
Mapping into a geometric realization.
Suppose $S$ is a simplicial set, $X$ is a space, and we are given a map
\[
f: \text{Sing}\,X\to S.
\]
When is is possible to produce a map $X\to |S|$?
We can take ...
- 569
0
votes
0
answers
179
views
semigroup actions of groups on regular rooted trees
If $G$ is a group which has a semigroup action on a regular rooted tree via prefix-preserving, continuous transformations (I give the tree the path metric), what kinds of algebraic restrictions can we ...
- 125
2
votes
0
answers
409
views
virtual bundle with compact support
A virtual bundle with compact support is a triple $E$={$E_1$,$E_2$,$a$},
where $E_1$ and $E_2$ are bundles over $M$ of the same dimension, $M$ is a closed manifold, $a$ is a bundle map from $E_1$ to $...
- 381
3
votes
1
answer
187
views
Examples of H-cogroups and a question about julia sets
The following questions should be very easy, but I need help. Notations are same as Bredon's geometry and topology book. This question is related to chapter VII.3.page 441.
$\nabla \colon X\vee X\...
- 244
3
votes
0
answers
236
views
Mapping from $X$ to $S^4$
I asked this question previously on stackexchange (https://math.stackexchange.com/questions/18668/mapping-from-x-to-s4) but could not get a solution. Any help is appreciated.
The question is (...
- 31
1
vote
0
answers
45
views
Equivalence between the definitions of Reidemeister Coincidence number
Given two applications $f$ and $g$, denote by $R (f, g)$ the set of Reidemeister classes determined by $f$ and $g$ (according to the algebraic definition, on the induced on fundamental groups). And $\...
- 29
4
votes
1
answer
149
views
singular cohomological dimension
Let $X$ be a finite CW complex. Is there an integer $N,$ such that $H^i(X,F)=0$ for all $i>N$ and all abelian sheaves $F$ on $X?$ The cohomology is defined to be the derived functor of the global ...
- 4,265
5
votes
1
answer
190
views
Adapting families of diffeomorphisms to an open cover
Has anyone seen the following result in the literature? I've asked a few experts but so far I've come up with nothing.
Given a manifold M and an open cover {U_i} ...
- 12.8k
0
votes
0
answers
109
views
finiteness of the dimensions of cohomologies of open subsets of a compact manifold
Let $M$ be a compact differentiable manifold which can be covered by two open subsets $U$ and $V$. Then $H_{\text{dR}}^n(M)$ is finite-dimensional for all $n$. But how about $U$, $V$ and $U\cap V$? ...
3
votes
0
answers
124
views
$B\Gamma$ constructed
In his pioneering paper on foliations, Haefliger obtains $B\Gamma_q$
as the representing space of a functor, NOT by construction analogous to the bar construction.
Who made that connection first? Bott?...
- 3,880
0
votes
1
answer
251
views
altering curvature on a tessellation representation of a compact surface
I have been reading about tessellation representations of compact surfaces, such as how the square tiling the plane represents the torus. For surfaces of genus > 1 (the ones that interest me), we ...
1
vote
0
answers
193
views
How to get countably many generators for $K_{j}^{G}(\beta G)$ ??
Hey
I am trying to find out how the Baum-Connes conjecture works over $GL(1)$ over local fiels.
I am just wondering if anybody knows how to get a countable many generators for in the L.H.S of the ...
- 85
5
votes
0
answers
350
views
Chain/Hierarchy of Monoids
Let's assume that we have the following collection of structures:
Some space $P$.
Monoids $(M_{i+1},\circ_{i+1})$, and
Actions $\bullet_{i+1}:M_{i+1}\times M_i\to M_i$, for $i\ge 0$
And $\bullet_{0}:...
- 1,882
8
votes
0
answers
340
views
Do p-compact groups have a sufficiently good notion of "flag variety" and "intersection cohomology"?
This is mostly an idle question, since I don't think I'd be able to do anything with a positive answer. But a positive answer would still be interesting, I think.
Background
An outstanding problem ...
- 118k
0
votes
0
answers
60
views
Relative homology of interlevel set
Let us consider a function $f:\mathbb{R}^3→\mathbb{R}$,
$f(x,y,z)=x^3+y^3+z^3-5yz$. Can anybody drop a hint how
to compute relative homology of interlevel sets with coefficients in $\mathbb{R}:
H_{\...
- 181
2
votes
0
answers
250
views
Examples of weakly nullhomologous cycles on smooth manifolds
Suppose X is a smooth manifold with homology groups H_p(X). For example let X be an open subset of Euclidean space.
What would be natural examples of cycles that are "weakly homologous to zero" but ...
0
votes
1
answer
219
views
Cofibrations of differential graded commutative algebras
Let $X$ a smooth manifold. Is the pullback morphism
$\Omega^\bullet(X)\to\Omega^\bullet(X\times \mathbb{R}^n)$ an acyclic cofibration of differential graded commutative algebras? I guess so, and even ...
- 6,777
7
votes
0
answers
297
views
Inner product on Hochschild homology in 2d TCFTs
This should be an easy question for some people. Take a compact $A(\infty)$ algebra with a cyclically symmetric non-degenerate inner product. In Kontsevich and Soibelman's article "Notes on $A(\infty)$...
- 3,758
2
votes
0
answers
129
views
spaces of projections
Let $\mathbb{K}$ be the compact operators on a separable infinite dimensional Hilbert space. Denote by $\mathcal{P}(\mathbb{K})$ the space of projections in $\mathbb{K}$. If I am not terribly wrong ...
- 7,637
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
0
votes
1
answer
147
views
Small set of acts over a countable monoid?
Given a countable monoid $S$, is the set of all (isomorphic representatives of) $S$-acts a small set?
- 11
0
votes
2
answers
172
views
small extensions of the free semigroup of rank 1
Let N denote the free semigroup of rank 1. Say that a semigroup T is a small extension
of N if N embeds in T and |T - N| is finite. Is there some kind of classification
of small extensions of N? ...
- 91
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
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
1
vote
1
answer
154
views
undecidability in the dynamics of functions $f: \Sigma^* \rightarrow \Sigma^*$
Does anyone know any undecidable problems in the dynamics of functions (not necessarily monoid homomorphisms or anything) from \Sigma^* to \Sigma^* where \Sigma is a finite set? In particular, I'm ...
- 549
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
0
votes
0
answers
85
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
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
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