User Akela

58 votes

1 answer

13k views

Is the Green-Tao theorem true for primes within a given arithmetic progression?

asked May 20, 2010 at 18:36

38 votes

3 answers

11k views

Why do the homology groups capture holes in a space better than the homotopy groups?

asked May 14, 2010 at 22:43

30 votes

3 answers

3k views

What is special about polylogarithms that leads to so many interesting identities and applications?

asked May 20, 2010 at 21:27

28 votes

5 answers

11k views

(Co)homology of the Eilenberg-MacLane spaces K(G,n)

asked May 15, 2010 at 14:15

16 votes

2 answers

2k views

Is a conceptual explanation possible for why the space of 1-forms on a manifold captures all its geometry?

asked May 20, 2010 at 16:26

15 votes

6 answers

5k views

Fundamental group of the line with the double origin.

asked May 21, 2010 at 11:57

13 votes

3 answers

4k views

Why are integrals over cycles called periods?

asked May 20, 2010 at 14:31

13 votes

3 answers

3k views

Are there applications of algebraic geometry into algebraic topology?

asked May 19, 2010 at 21:24

13 votes

3 answers

2k views

Ways of formulating homological algebra without diagram chasing

asked May 15, 2010 at 8:35

12 votes

4 answers

3k views

Zariski closed sets in C^n are of measure 0

asked May 21, 2010 at 17:48

12 votes

3 answers

1k views

Relevance of the complex structure of a function algebra for capturing the topology on a space.

asked May 25, 2010 at 14:07

10 votes

2 answers

1k views

Why the choice of the simplex for defining homology?

asked May 16, 2010 at 21:31

9 votes

2 answers

3k views

Differentiable structures on R^3

asked May 16, 2010 at 20:42

9 votes

4 answers

4k views

Canonical fundamental domain for a discrete subgroup Γ of SL₂(R) acting on hyperbolic plane

asked May 23, 2010 at 15:38

8 votes

2 answers

1k views

The word "torsion" and its connection to geometry and homology

asked May 25, 2010 at 12:05

8 votes

1 answer

3k views

Why are order-k differential forms sections of the kth exterior power of the cotangent bundle?

asked May 15, 2010 at 9:28

8 votes

2 answers

4k views

How does singular homology H_n capture the number of n-dimensional "holes" in a space?

asked May 12, 2010 at 23:50

7 votes

1 answer

606 views

Precise relation between prime number theorem and zero-free region

asked May 24, 2010 at 17:44

5 votes

4 answers

2k views

Distributions more complicated than the Dirac δ and derivatives

asked May 21, 2010 at 22:41

5 votes

1 answer

2k views

How to compute the (co)homology of a compact Riemann surface?

asked May 19, 2010 at 21:10

4 votes

2 answers

337 views

Determining the field from the topology of the affine space over it.

asked May 21, 2010 at 17:47

3 votes

1 answer

290 views

What is the order of differentiability of the tangent bundle of a C^2- manifold?

asked May 17, 2010 at 12:56

3 votes

3 answers

417 views

Why is continuity required for sheaf-theoretic definitions of a structure on a space

asked May 19, 2010 at 13:32

3 votes

4 answers

565 views

How to determine explicit description for a projective variety?

asked May 19, 2010 at 22:26

3 votes

1 answer

1k views

Does there exist a classification of covering spaces in algebraic geometry?

asked May 11, 2010 at 18:31

3 votes

3 answers

560 views

Counting connected manifolds

asked May 16, 2010 at 21:01

2 votes

2 answers

684 views

Domains of holomorphy in the complex plane

asked May 12, 2010 at 23:25

1 vote

1 answer

168 views

Does there exists a (possibly homological) characterization of the Jordan curve property in all dimensions?

asked May 16, 2010 at 14:38

Stack Exchange Network

28 Questions

Is the Green-Tao theorem true for primes within a given arithmetic progression?

Why do the homology groups capture holes in a space better than the homotopy groups?

What is special about polylogarithms that leads to so many interesting identities and applications?

(Co)homology of the Eilenberg-MacLane spaces K(G,n)

Is a conceptual explanation possible for why the space of 1-forms on a manifold captures all its geometry?

Fundamental group of the line with the double origin.

Why are integrals over cycles called periods?

Are there applications of algebraic geometry into algebraic topology?

Ways of formulating homological algebra without diagram chasing

Zariski closed sets in C^n are of measure 0

Relevance of the complex structure of a function algebra for capturing the topology on a space.

Why the choice of the simplex for defining homology?

Differentiable structures on R^3

Canonical fundamental domain for a discrete subgroup Γ of SL₂(R) acting on hyperbolic plane

The word "torsion" and its connection to geometry and homology

Why are order-k differential forms sections of the kth exterior power of the cotangent bundle?

How does singular homology H_n capture the number of n-dimensional "holes" in a space?

Precise relation between prime number theorem and zero-free region

Distributions more complicated than the Dirac δ and derivatives

How to compute the (co)homology of a compact Riemann surface?

Determining the field from the topology of the affine space over it.

What is the order of differentiability of the tangent bundle of a C^2- manifold?

Why is continuity required for sheaf-theoretic definitions of a structure on a space

How to determine explicit description for a projective variety?

Does there exist a classification of covering spaces in algebraic geometry?

Counting connected manifolds

Domains of holomorphy in the complex plane

Does there exists a (possibly homological) characterization of the Jordan curve property in all dimensions?