User Allen Hatcher

86 votes

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Why do finite homotopy groups imply finite homology groups?

answered Dec 20, 2009 at 14:01

82 votes

Learning Topology

answered Dec 11, 2009 at 16:35

79 votes

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Maps which induce the same homomorphism on homotopy and homology groups are homotopic

answered Feb 5, 2015 at 22:41

77 votes

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Definition of "simplicial complex"

answered Nov 20, 2009 at 19:02

75 votes

Periods and commas in mathematical writing

answered Nov 25, 2009 at 16:24

73 votes

Homotopy groups of Lie groups

answered Dec 15, 2009 at 15:32

60 votes

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Intuition behind Thom class

answered Sep 22, 2012 at 21:06

51 votes

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Triangulating surfaces

answered Dec 13, 2013 at 16:33

48 votes

Spectral sequences: opening the black box slowly with an example

answered Nov 6, 2010 at 9:23

44 votes

Colloquial catchy statements encoding serious mathematics

answered Apr 19, 2011 at 4:11

43 votes

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nontrivial $\pi_2(\textrm{Diff}(M))$

answered May 24, 2012 at 11:26

41 votes

Parallelizability of the Milnor's exotic spheres in dimension 7

answered Mar 11, 2011 at 17:45

35 votes

Why do wedges of spheres often appear in combinatorics?

answered Mar 7, 2010 at 16:12

35 votes

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

answered May 15, 2010 at 14:51

34 votes

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Are there pairs of highly connected finite CW-complexes with the same homotopy groups?

answered Nov 13, 2009 at 20:00

32 votes

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Survey articles on homotopy groups of spheres

answered May 14, 2010 at 14:07

32 votes

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What characteristic class information comes from the 2-torsion of $H^*(BSO(n);Z)$?

answered Mar 1, 2011 at 0:12

31 votes

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Fundamental group of the line with the double origin.

answered May 22, 2010 at 14:14

30 votes

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Fibers of fibrations of a 3-manifold over $S^1$

answered Apr 8, 2011 at 1:48

28 votes

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Is the space of diffeomorphisms homotopy equivalent to a CW-complex?

answered Apr 8, 2013 at 22:49

28 votes

How to compute $\pi_{3}$ of $L(p,q)\# L(p',q')$?

answered Oct 30, 2014 at 21:08

28 votes

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Unique smooth structure on 3-manifolds

answered Mar 26, 2018 at 1:01

26 votes

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Homology equivalence and isomorphism on $\pi_1$ not enough for homotopy equivalence?

answered Feb 15, 2015 at 15:46

24 votes

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Points on a sphere

answered Jun 1, 2010 at 15:50

24 votes

Reference for a fact (?) on homeomorphic knot complements

answered Oct 30, 2014 at 18:20

23 votes

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how to visualize the class number of an imaginary quadratic field?

answered Apr 17, 2013 at 3:03

22 votes

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Detecting homotopy nontriviality of an element in a torsion homotopy group

answered Apr 13, 2013 at 2:38

22 votes

CW-structures and Morse functions: a reference request

answered Jan 11, 2010 at 3:07

21 votes

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An elementary proof that the degree of a map of spheres determines its homotopy type

answered May 21, 2010 at 22:06

20 votes

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The Wedge Sum of path connected topological spaces

answered Jul 3, 2010 at 22:30

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114 Answers

Why do finite homotopy groups imply finite homology groups?

Learning Topology

Maps which induce the same homomorphism on homotopy and homology groups are homotopic

Definition of "simplicial complex"

Periods and commas in mathematical writing

Homotopy groups of Lie groups

Intuition behind Thom class

Triangulating surfaces

Spectral sequences: opening the black box slowly with an example

Colloquial catchy statements encoding serious mathematics

nontrivial $\pi_2(\textrm{Diff}(M))$

Parallelizability of the Milnor's exotic spheres in dimension 7

Why do wedges of spheres often appear in combinatorics?

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

Are there pairs of highly connected finite CW-complexes with the same homotopy groups?

Survey articles on homotopy groups of spheres

What characteristic class information comes from the 2-torsion of $H^*(BSO(n);Z)$?

Fundamental group of the line with the double origin.

Fibers of fibrations of a 3-manifold over $S^1$

Is the space of diffeomorphisms homotopy equivalent to a CW-complex?

How to compute $\pi_{3}$ of $L(p,q)\# L(p',q')$?

Unique smooth structure on 3-manifolds

Homology equivalence and isomorphism on $\pi_1$ not enough for homotopy equivalence?

Points on a sphere

Reference for a fact (?) on homeomorphic knot complements

how to visualize the class number of an imaginary quadratic field?

Detecting homotopy nontriviality of an element in a torsion homotopy group

CW-structures and Morse functions: a reference request

An elementary proof that the degree of a map of spheres determines its homotopy type

The Wedge Sum of path connected topological spaces