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13 votes

Is the Hurewicz theorem ever used to compute abelianizations?

answered Jan 26, 2017 at 18:47

13 votes

Which stable homotopy groups are represented by parallelizable manifolds?

answered Jun 26, 2020 at 23:29

13 votes

Accepted

On the state of the art on closed $(n-1)$-connected $2n$ manifolds

answered Jan 12, 2021 at 16:23

11 votes

Accepted

Characteristic classes of non-linear sphere bundles

answered Jun 29, 2022 at 12:15

11 votes

Accepted

Mapping class groups in high dimension

answered Jun 9, 2019 at 0:40

11 votes

What are examples when the equality of some invariants is good enough in algebraic topology?

answered Sep 18, 2015 at 14:34

8 votes

cohomology of BG, G compact Lie group

answered Mar 14, 2014 at 14:10

6 votes

Accepted

Classifying spaces of topological groups whose underlying spaces are homotopy equivalent

answered Mar 31, 2015 at 20:04

6 votes

A $\mathbb{R}^{n}$ -fiber bundle which do not admit a n-dimensional vector bundle structure

answered Oct 27, 2016 at 7:43

6 votes

Accepted

Naive G-spectrum representing geometric equivariant cobordism

answered Jun 1, 2015 at 17:30

6 votes

Why is $Lex(\mathcal{A},\mathcal{Ab})$ abelian? Does $Lex(\mathcal{A},\mathcal{Ab})\rightarrow Func(\mathcal{A},\mathcal{Ab})$ admit a left-adjoint?

answered May 11, 2013 at 16:18

5 votes

$\pi_{2n-1}(\operatorname{SO}(2n))$ element represents the tangent bundle $TS^{2n}$, not torsion and indivisible for $n>1$?

answered May 3, 2021 at 19:49

4 votes

Accepted

Stable cohomology of mapping class group with coefficients in $H^{\otimes n}$

answered Sep 21, 2022 at 12:09

4 votes

Accepted

Version of pseudo-isotopy $\neq$ isotopy for $(n+1)$-framings

answered Nov 5, 2023 at 10:24

4 votes

connected compact semisimple lie group finite fundamental group

answered Mar 9, 2013 at 17:46

3 votes

Geometric realization of simplicial spaces and finite limits

answered Aug 12, 2015 at 14:39

2 votes

Decomposition of solvable Lie group

answered Mar 26, 2013 at 1:21

1 vote

Homology of loop space

answered May 25, 2015 at 10:43

1 vote

Generalize $\pi_0(B\mathcal{C})\cong\{\text{objects}\}/\{\text{morphisms}\}$ to categories internal to topological spaces

answered Aug 12, 2015 at 15:12

1 vote

The reflexive free-category comonad-resolution is a cofibrant replacement of the discrete simplicial category associated with an ordinary category in the Bergner model structure on the category of small simplicial categories?

answered Jun 12, 2017 at 21:21

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20 Answers

Is the Hurewicz theorem ever used to compute abelianizations?

Which stable homotopy groups are represented by parallelizable manifolds?

On the state of the art on closed $(n-1)$-connected $2n$ manifolds

Characteristic classes of non-linear sphere bundles

Mapping class groups in high dimension

What are examples when the equality of some invariants is good enough in algebraic topology?

cohomology of BG, G compact Lie group

Classifying spaces of topological groups whose underlying spaces are homotopy equivalent

A $\mathbb{R}^{n}$ -fiber bundle which do not admit a n-dimensional vector bundle structure

Naive G-spectrum representing geometric equivariant cobordism

Why is $Lex(\mathcal{A},\mathcal{Ab})$ abelian? Does $Lex(\mathcal{A},\mathcal{Ab})\rightarrow Func(\mathcal{A},\mathcal{Ab})$ admit a left-adjoint?

$\pi_{2n-1}(\operatorname{SO}(2n))$ element represents the tangent bundle $TS^{2n}$, not torsion and indivisible for $n>1$?

Stable cohomology of mapping class group with coefficients in $H^{\otimes n}$

Version of pseudo-isotopy $\neq$ isotopy for $(n+1)$-framings

connected compact semisimple lie group finite fundamental group

Geometric realization of simplicial spaces and finite limits

Decomposition of solvable Lie group

Homology of loop space

Generalize $\pi_0(B\mathcal{C})\cong\{\text{objects}\}/\{\text{morphisms}\}$ to categories internal to topological spaces

The reflexive free-category comonad-resolution is a cofibrant replacement of the discrete simplicial category associated with an ordinary category in the Bergner model structure on the category of small simplicial categories?