User Achim Krause

58 votes

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Is there any use for $\sin(\sin x)$?

answered Feb 1, 2021 at 19:23

38 votes

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Simply-connected rational homology spheres

answered Aug 13, 2015 at 17:30

37 votes

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If $\Omega X \simeq \Omega Y$ then is $X \simeq Y$ for $X,Y$ simply connected?

answered Nov 22, 2019 at 13:26

32 votes

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What is the group of pointed homotopy classes of maps from $S^3 \times S^3$ to $S^3$?

answered Mar 14, 2014 at 6:54

29 votes

What should I call a "differential" which cubes, rather than squares, to zero?

answered Mar 24, 2020 at 19:10

24 votes

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Does the isomorphic of the fundamental groups imply the existence of a mapping inducing an isomorphism?

answered Nov 10, 2021 at 6:39

22 votes

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Is $[X, \_]$ a homology theory?

answered May 21, 2020 at 23:00

18 votes

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Is $SU(3)/SO(3)$ cobordant with a mapping torus?

answered Apr 29, 2014 at 8:07

16 votes

What is the first interesting matric Toda bracket in the stable homotopy of the sphere?

answered Mar 9, 2014 at 6:11

16 votes

Which singular homology classes can be represented by embedded manifolds?

answered Oct 26, 2020 at 12:43

16 votes

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When is the augmentation ideal projective as RG-module?

answered Jun 16, 2021 at 20:30

15 votes

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Hairy ball theorem for odd-dimensional spheres

answered Feb 24, 2019 at 16:45

15 votes

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Identifying two definitions of orientation on a vector space

answered Mar 28 at 19:47

14 votes

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Direct limits in homotopy category

answered Aug 12 at 12:08

14 votes

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What does Robert Stong mean when he says $H^*(MO(k))$ is a free Steenrod algebra in dimension less than $2k$?

answered Dec 2 at 7:31

14 votes

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loop space of a finite CW-complex

answered Sep 4, 2020 at 14:28

14 votes

Simplest example of non-trivial Toda bracket in spaces

answered Jul 1, 2014 at 19:51

14 votes

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

answered Feb 15, 2015 at 7:42

14 votes

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Why are ordinary spheres not strictly invertible?

answered Feb 5, 2023 at 17:02

13 votes

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Does there exist a Bousfield localization of the category of spectra which makes the sphere unbounded below?

answered Apr 15 at 17:50

13 votes

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Abelian categories satisfying AB5*

answered Aug 20, 2023 at 8:27

12 votes

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Why isn't the anchor map in Lurie's "Rotation Invariance in Algebraic K-Theory" zero?

answered Mar 8, 2023 at 6:37

12 votes

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Motivation for the definition of complex orientable cohomology theory

answered Feb 11, 2021 at 9:46

11 votes

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Lifting of map from $S^3$ to itself

answered Feb 27 at 21:58

10 votes

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How many roots do $\tan(z)-z^n = 0$, $\sin(z)-z^n=0, \ \cos(z)-z^n=0, $ have?

answered Aug 17 at 13:01

10 votes

Boundedness of sum of sin(sin(n))

answered Aug 5 at 11:42

10 votes

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RIng that is flat over a subring as a right module but not as a left module

answered Oct 13, 2021 at 11:08

10 votes

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Is every map from a simplicial complex to a sphere homotopic to a simplicial map to the boundary of a k-simplex?

answered Jun 11, 2021 at 17:08

10 votes

In the not necessarily abelian cat setting, is there a Grothendieck spectral sequence for computing the homotopy of a composition of derived functors?

answered Mar 6, 2022 at 9:33

10 votes

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Are algebras of smooth functions formally smooth?

answered Nov 22, 2022 at 9:27

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113 Answers

Is there any use for $\sin(\sin x)$?

Simply-connected rational homology spheres

If $\Omega X \simeq \Omega Y$ then is $X \simeq Y$ for $X,Y$ simply connected?

What is the group of pointed homotopy classes of maps from $S^3 \times S^3$ to $S^3$?

What should I call a "differential" which cubes, rather than squares, to zero?

Does the isomorphic of the fundamental groups imply the existence of a mapping inducing an isomorphism?

Is $[X, \_]$ a homology theory?

Is $SU(3)/SO(3)$ cobordant with a mapping torus?

What is the first interesting matric Toda bracket in the stable homotopy of the sphere?

Which singular homology classes can be represented by embedded manifolds?

When is the augmentation ideal projective as RG-module?

Hairy ball theorem for odd-dimensional spheres

Identifying two definitions of orientation on a vector space

Direct limits in homotopy category

What does Robert Stong mean when he says $H^*(MO(k))$ is a free Steenrod algebra in dimension less than $2k$?

loop space of a finite CW-complex

Simplest example of non-trivial Toda bracket in spaces

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

Why are ordinary spheres not strictly invertible?

Does there exist a Bousfield localization of the category of spectra which makes the sphere unbounded below?

Abelian categories satisfying AB5*

Why isn't the anchor map in Lurie's "Rotation Invariance in Algebraic K-Theory" zero?

Motivation for the definition of complex orientable cohomology theory

Lifting of map from $S^3$ to itself

How many roots do $\tan(z)-z^n = 0$, $\sin(z)-z^n=0, \ \cos(z)-z^n=0, $ have?

Boundedness of sum of sin(sin(n))

RIng that is flat over a subring as a right module but not as a left module

Is every map from a simplicial complex to a sphere homotopic to a simplicial map to the boundary of a k-simplex?

In the not necessarily abelian cat setting, is there a Grothendieck spectral sequence for computing the homotopy of a composition of derived functors?

Are algebras of smooth functions formally smooth?