User Johannes Ebert

107 votes

Parallelizability of the Milnor's exotic spheres in dimension 7

answered Mar 11, 2011 at 10:48

95 votes

Proofs that require fundamentally new ways of thinking

answered Dec 9, 2010 at 19:42

64 votes

Accepted

Is there a sheaf theoretical characterization of a differentiable manifold?

answered Feb 10, 2012 at 9:46

56 votes

Books you would like to read (if somebody would just write them…)

answered Jan 24, 2011 at 14:07

36 votes

What is the exterior derivative intuitively?

answered Feb 19, 2011 at 18:52

36 votes

Accepted

Relative De Rham cohomologies

answered Oct 30, 2012 at 9:46

34 votes

Accepted

What is the intuition behind the Freudenthal suspension theorem?

answered Feb 23, 2011 at 20:42

32 votes

What do the stable homotopy groups of spheres say about the combinatorics of finite sets?

answered Feb 28, 2012 at 10:26

30 votes

Accepted

Are infinite dimensional constructions needed to prove finite dimensional results?

answered Feb 17, 2011 at 23:37

25 votes

Motivating the de Rham theorem

answered Oct 26, 2010 at 17:23

25 votes

Non-vanishing of group cohomology in sufficiently high degree

answered May 11, 2011 at 20:45

25 votes

Accepted

Example of an unstable map between finite complexes which is the identity on homotopy but not homotopic to the identity?

answered Dec 22, 2017 at 6:54

24 votes

Accepted

Vanishing of $\hat{A}$ genus and positive scalar curvature

answered Sep 28, 2011 at 21:13

23 votes

Accepted

Is there a map of spectra implementing the Thom isomorphism?

answered Nov 21, 2010 at 10:50

22 votes

Euler characteristic of orbifolds

answered Jan 13, 2011 at 20:09

22 votes

Accepted

If the universal cover of a manifold is spin, must it admit a finite cover which is spin?

answered Sep 8, 2020 at 18:27

21 votes

Accepted

Universal property of the tangent bundle

answered Feb 13, 2011 at 15:54

21 votes

Accepted

How does the group algebra look as a Lie algebra

answered Apr 3, 2011 at 16:53

20 votes

Awfully sophisticated proof for simple facts

answered Dec 21, 2012 at 19:13

19 votes

What are "good" examples of spin manifolds?

answered Nov 4, 2011 at 22:08

19 votes

Coefficients in cohomology

answered Apr 30, 2011 at 14:37

19 votes

Ways to prove the fundamental theorem of algebra

answered Oct 17, 2010 at 13:50

18 votes

Most intricate and most beautiful structures in mathematics

answered Dec 17, 2010 at 10:32

18 votes

Is there a Chern-Gauss-Bonnet theorem for orbifolds?

answered Jan 26, 2011 at 13:31

17 votes

Is this a "folk theorem" about analytic functions of a complex variable?

answered Oct 24, 2012 at 19:07

17 votes

Accepted

Manifolds with prescribed fundamental group and finitely many trivial homotopy groups

answered Oct 13, 2012 at 13:14

17 votes

What are your favorite instructional counterexamples?

answered Mar 24, 2013 at 5:44

16 votes

Accepted

Homotopy spheres with vanishing and non-vanishing $\alpha$-invariant

answered Jun 16, 2014 at 16:40

16 votes

Accepted

Acyclic aspherical spaces with acyclic fundamental groups

answered Nov 28, 2017 at 21:09

16 votes

Accepted

Mysterious property of $\mathbb{Q}$

answered Apr 12, 2012 at 20:43

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188 Answers

Parallelizability of the Milnor's exotic spheres in dimension 7

Proofs that require fundamentally new ways of thinking

Is there a sheaf theoretical characterization of a differentiable manifold?

Books you would like to read (if somebody would just write them…)

What is the exterior derivative intuitively?

Relative De Rham cohomologies

What is the intuition behind the Freudenthal suspension theorem?

What do the stable homotopy groups of spheres say about the combinatorics of finite sets?

Are infinite dimensional constructions needed to prove finite dimensional results?

Motivating the de Rham theorem

Non-vanishing of group cohomology in sufficiently high degree

Example of an unstable map between finite complexes which is the identity on homotopy but not homotopic to the identity?

Vanishing of $\hat{A}$ genus and positive scalar curvature

Is there a map of spectra implementing the Thom isomorphism?

Euler characteristic of orbifolds

If the universal cover of a manifold is spin, must it admit a finite cover which is spin?

Universal property of the tangent bundle

How does the group algebra look as a Lie algebra

Awfully sophisticated proof for simple facts

What are "good" examples of spin manifolds?

Coefficients in cohomology

Ways to prove the fundamental theorem of algebra

Most intricate and most beautiful structures in mathematics

Is there a Chern-Gauss-Bonnet theorem for orbifolds?

Is this a "folk theorem" about analytic functions of a complex variable?

Manifolds with prescribed fundamental group and finitely many trivial homotopy groups

What are your favorite instructional counterexamples?

Homotopy spheres with vanishing and non-vanishing $\alpha$-invariant

Acyclic aspherical spaces with acyclic fundamental groups

Mysterious property of $\mathbb{Q}$