User user43326

17 votes

(co)homology of symmetric groups

answered Sep 11, 2014 at 16:19

15 votes

Abstract proof that $\lvert H^2(G,A)\rvert$ counts group extensions

answered May 10, 2019 at 17:58

11 votes

Accepted

Why does the Steenrod algebra act faithfully on $H^\ast(BC_p)$?

answered Dec 13, 2019 at 7:41

10 votes

Accepted

Representation of finite groups in a compact Lie group

answered Jul 26, 2014 at 13:02

8 votes

Accepted

Equivalence of the total spaces of two Serre fibrations with equivalent fibers

answered Jun 26, 2014 at 14:23

8 votes

Accepted

What is $Sq^i(\alpha^j)$ for all $i$ and $j$?

answered Jul 16, 2015 at 16:44

8 votes

Accepted

Atiyah Bott-Shapiro orientation Vs Anderson-Brown-Peterson Splitting

answered Feb 2, 2018 at 18:21

7 votes

Accepted

cohomology of iterated loop space on spheres

answered Aug 31, 2015 at 14:04

7 votes

Accepted

What are the cohomology groups $H^d(BSO_\infty,Z)$ and $H^d(BO_\infty,Z)$?

answered May 7, 2014 at 8:12

6 votes

Accepted

Reference for: $p$-primary component of $\pi^S_k$ is $\Bbb Z_p$ when $k=2l(p-1)-1$

answered Jul 29, 2018 at 7:18

6 votes

Thom space, homotopy group and cohomology group

answered Aug 14, 2018 at 7:20

5 votes

Group (Co)Homology of Symmetric Group

answered Apr 13, 2018 at 6:49

5 votes

Accepted

Is there a geometric interpretation of Johnson-Wilson E(n) analogous to vector bundles for K-theory?

answered May 30, 2014 at 15:02

5 votes

Accepted

Equivalence of homotopy categories and model structure theory

answered Feb 9, 2014 at 10:36

5 votes

Decompose $MT(E(d)\times_{\mathbb Z_2} SU(2))$ as the wedge sum or smash product of spectra

answered Apr 30, 2019 at 5:47

5 votes

Accepted

Cohomology algebra of a fibration whose spectral sequence degenerates in the second term

answered Dec 25, 2019 at 11:56

5 votes

The homology of the universal covering space, why so difficult to compute

answered Mar 17, 2020 at 20:21

5 votes

What are your favorite instructional counterexamples?

answered Oct 21, 2022 at 13:06

4 votes

Accepted

The Thom map for the Brown-Peterson cohomology

answered Jun 30, 2020 at 15:02

4 votes

Using Stiefel-Whitney class to build new principal bundles

answered Jun 25, 2019 at 18:58

4 votes

Group cohomology of $S_3$ in terms of its Sylow subgroups

answered Apr 17, 2019 at 7:20

4 votes

Accepted

Reference requests: Integral cohomology of $G_2$-homogeneous spaces

answered Apr 22, 2019 at 13:43

4 votes

cohomology of classifying space of permutation groups

answered Oct 20, 2014 at 8:12

4 votes

Isomorphism between the Burnside ring $A(G)$ and the zeroth $G$-equivariant stable homotopy $\pi^{G}_0(S^0)$

answered Jan 2, 2015 at 9:33

4 votes

Accepted

spectral sequence with non-trivial action on coefficients

answered Jun 4, 2014 at 8:55

4 votes

All mapping space between CW complexes is a CW complex?

answered Dec 27, 2013 at 8:57

4 votes

Connective spectra and infinite loop spaces

answered Sep 13, 2017 at 7:06

4 votes

Accepted

Spin cobordism v.s. KO theory in low or in any dimensions

answered Oct 22, 2018 at 16:44

4 votes

Accepted

coproduct of the homology of iterated loop space on spheres

answered Aug 9, 2015 at 14:56

4 votes

Accepted

group completion theorem of homology as Hopf algebras

answered Aug 21, 2015 at 14:08

Stack Exchange Network

53 Answers

(co)homology of symmetric groups

Abstract proof that $\lvert H^2(G,A)\rvert$ counts group extensions

Why does the Steenrod algebra act faithfully on $H^\ast(BC_p)$?

Representation of finite groups in a compact Lie group

Equivalence of the total spaces of two Serre fibrations with equivalent fibers

What is $Sq^i(\alpha^j)$ for all $i$ and $j$?

Atiyah Bott-Shapiro orientation Vs Anderson-Brown-Peterson Splitting

cohomology of iterated loop space on spheres

What are the cohomology groups $H^d(BSO_\infty,Z)$ and $H^d(BO_\infty,Z)$?

Reference for: $p$-primary component of $\pi^S_k$ is $\Bbb Z_p$ when $k=2l(p-1)-1$

Thom space, homotopy group and cohomology group

Group (Co)Homology of Symmetric Group

Is there a geometric interpretation of Johnson-Wilson E(n) analogous to vector bundles for K-theory?

Equivalence of homotopy categories and model structure theory

Decompose $MT(E(d)\times_{\mathbb Z_2} SU(2))$ as the wedge sum or smash product of spectra

Cohomology algebra of a fibration whose spectral sequence degenerates in the second term

The homology of the universal covering space, why so difficult to compute

What are your favorite instructional counterexamples?

The Thom map for the Brown-Peterson cohomology

Using Stiefel-Whitney class to build new principal bundles

Group cohomology of $S_3$ in terms of its Sylow subgroups

Reference requests: Integral cohomology of $G_2$-homogeneous spaces

cohomology of classifying space of permutation groups

Isomorphism between the Burnside ring $A(G)$ and the zeroth $G$-equivariant stable homotopy $\pi^{G}_0(S^0)$

spectral sequence with non-trivial action on coefficients

All mapping space between CW complexes is a CW complex?

Connective spectra and infinite loop spaces

Spin cobordism v.s. KO theory in low or in any dimensions

coproduct of the homology of iterated loop space on spheres

group completion theorem of homology as Hopf algebras