User Grigory M - Mathematics Stack Exchange

34 votes

Accepted

Which manifolds are parallelizable?

answered Jun 19, 2011 at 15:47

30 votes

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Combinatorial proof of a Stirling number identity.

answered May 23, 2013 at 11:12

29 votes

Solution to $1-f(x) = f(-x)$

answered Jul 30, 2010 at 8:32

28 votes

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Is there a direct proof of this lcm identity?

answered Aug 5, 2010 at 19:44

26 votes

Are there any Hessian matrices that are asymmetric on a large set?

answered Jun 26, 2011 at 19:17

26 votes

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Geometric interpretation of the cofactor expansion theorem

answered Dec 5, 2013 at 19:38

25 votes

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Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$

answered Jun 2, 2011 at 15:41

25 votes

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How do you prove that a group specified by a presentation is infinite?

answered Jul 23, 2010 at 17:41

24 votes

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Non-orientable 3-manifold has infinite fundamental group

answered Jun 16, 2013 at 9:57

23 votes

Why isn't $\mathbb{CP}^2$ a covering space for any other manifold?

answered Apr 1, 2011 at 18:09

22 votes

Why is the volume of a cone one third of the volume of a cylinder?

answered Jul 24, 2010 at 7:30

20 votes

When characteristic classes determine a bundle?

answered May 3, 2014 at 20:32

19 votes

Surprising Generalizations

answered Aug 1, 2010 at 20:27

19 votes

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Maps between Eilenberg–MacLane spaces

answered Jun 4, 2011 at 6:47

19 votes

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How to compute homotopy classes of maps on the 2-torus?

answered May 2, 2011 at 20:11

18 votes

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What functor does $K(G, 1)$ represent for nonabelian $G$?

answered Apr 30, 2011 at 11:34

18 votes

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Why can't I combine complex powers

answered Aug 21, 2010 at 0:28

18 votes

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Why are the only associative division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?

answered Jul 23, 2010 at 8:32

17 votes

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About maps between homology groups

answered May 26, 2011 at 8:35

17 votes

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Is there a compact contractible manifold?

answered Jun 12, 2013 at 15:57

16 votes

Why homology with coefficients?

answered Dec 27, 2013 at 15:10

16 votes

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Is there a "counting groups/committees" proof for the identity $\binom{\binom{n}{2}}{2}=3\binom{n+1}{4}$?

answered Dec 26, 2014 at 14:05

15 votes

Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.

answered Dec 8, 2013 at 23:14

15 votes

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What's the loop space of a circle?

answered Jun 16, 2011 at 10:21

15 votes

If a manifold M has zero Euler characteristic, there is a non-vanishing vector field on it

answered Jun 25, 2011 at 8:09

15 votes

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Is it misleading to think of rank-2 tensors as matrices?

answered Aug 13, 2010 at 20:54

14 votes

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Two CW complexes with isomorphic homotopy groups and homology, yet not homotopy equivalent

answered Dec 6, 2011 at 18:06

14 votes

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Spaces with equal homotopy groups but different homology groups?

answered Jan 15, 2012 at 16:38

13 votes

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How do I count the subsets of a set whose number of elements is divisible by 3? 4?

answered Jul 28, 2010 at 8:25

13 votes

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Homology of the loop space

answered Jun 30, 2011 at 9:58

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207 Answers

Which manifolds are parallelizable?

Combinatorial proof of a Stirling number identity.

Solution to $1-f(x) = f(-x)$

Is there a direct proof of this lcm identity?

Are there any Hessian matrices that are asymmetric on a large set?

Geometric interpretation of the cofactor expansion theorem

Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$

How do you prove that a group specified by a presentation is infinite?

Non-orientable 3-manifold has infinite fundamental group

Why isn't $\mathbb{CP}^2$ a covering space for any other manifold?

Why is the volume of a cone one third of the volume of a cylinder?

When characteristic classes determine a bundle?

Surprising Generalizations

Maps between Eilenberg–MacLane spaces

How to compute homotopy classes of maps on the 2-torus?

What functor does $K(G, 1)$ represent for nonabelian $G$?

Why can't I combine complex powers

Why are the only associative division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?

About maps between homology groups

Is there a compact contractible manifold?

Why homology with coefficients?

Is there a "counting groups/committees" proof for the identity $\binom{\binom{n}{2}}{2}=3\binom{n+1}{4}$?

Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.

What's the loop space of a circle?

If a manifold M has zero Euler characteristic, there is a non-vanishing vector field on it

Is it misleading to think of rank-2 tensors as matrices?

Two CW complexes with isomorphic homotopy groups and homology, yet not homotopy equivalent

Spaces with equal homotopy groups but different homology groups?

How do I count the subsets of a set whose number of elements is divisible by 3? 4?

Homology of the loop space