User Akela

59 votes

1 answer

14k 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

12k views

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

asked May 14, 2010 at 22:43

28 votes

5 answers

12k views

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

asked May 15, 2010 at 14:15

15 votes

6 answers

6k views

Fundamental group of the line with the double origin.

asked May 21, 2010 at 11:57

14 votes

3 answers

5k views

Why are integrals over cycles called periods?

asked May 20, 2010 at 14:31

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

14 votes

4 answers

4k views

Zariski closed sets in C^n are of measure 0

asked May 21, 2010 at 17:48

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

10 votes

2 answers

3k views

Differentiable structures on R^3

asked May 16, 2010 at 20:42

13 votes

3 answers

3k views

Are there applications of algebraic geometry into algebraic topology?

asked May 19, 2010 at 21:24

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

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

5 votes

1 answer

2k views

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

asked May 19, 2010 at 21:10

14 votes

3 answers

2k views

Ways of formulating homological algebra without diagram chasing

asked May 15, 2010 at 8:35

17 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

5 votes

4 answers

2k views

Distributions more complicated than the Dirac δ and derivatives

asked May 21, 2010 at 22:41

11 votes

2 answers

2k views

Why the choice of the simplex for defining homology?

asked May 16, 2010 at 21:31

3 votes

1 answer

2k views

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

asked May 11, 2010 at 18:31

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

8 votes

2 answers

1k views

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

asked May 25, 2010 at 12:05

2 votes

2 answers

759 views

Domains of holomorphy in the complex plane

asked May 12, 2010 at 23:25

5 votes

3 answers

666 views

Counting connected manifolds

asked May 16, 2010 at 21:01

7 votes

1 answer

624 views

Precise relation between prime number theorem and zero-free region

asked May 24, 2010 at 17:44

3 votes

4 answers

613 views

How to determine explicit description for a projective variety?

asked May 19, 2010 at 22:26

3 votes

3 answers

455 views

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

asked May 19, 2010 at 13:32

4 votes

2 answers

365 views

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

asked May 21, 2010 at 17:47

3 votes

1 answer

356 views

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

asked May 17, 2010 at 12:56

1 vote

1 answer

169 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?

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

Fundamental group of the line with the double origin.

Why are integrals over cycles called periods?

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

Zariski closed sets in C^n are of measure 0

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

Differentiable structures on R^3

Are there applications of algebraic geometry into algebraic topology?

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

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

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

Ways of formulating homological algebra without diagram chasing

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

Distributions more complicated than the Dirac δ and derivatives

Why the choice of the simplex for defining homology?

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

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

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

Domains of holomorphy in the complex plane

Counting connected manifolds

Precise relation between prime number theorem and zero-free region

How to determine explicit description for a projective variety?

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

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?

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