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Achim Krause's user avatar
Achim Krause's user avatar
Achim Krause's user avatar
Achim Krause
  • Member for 10 years, 8 months
  • Last seen this week
57 votes
Accepted

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

38 votes
Accepted

Simply-connected rational homology spheres

37 votes
Accepted

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

32 votes
Accepted

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

29 votes

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

24 votes
Accepted

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

22 votes
Accepted

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

18 votes
Accepted

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

16 votes

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

16 votes

Which singular homology classes can be represented by embedded manifolds?

16 votes
Accepted

When is the augmentation ideal projective as RG-module?

15 votes
Accepted

Hairy ball theorem for odd-dimensional spheres

15 votes
Accepted

Identifying two definitions of orientation on a vector space

14 votes
Accepted

loop space of a finite CW-complex

14 votes

Simplest example of non-trivial Toda bracket in spaces

14 votes

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

14 votes
Accepted

Why are ordinary spheres not strictly invertible?

13 votes
Accepted

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

13 votes
Accepted

Abelian categories satisfying AB5*

12 votes
Accepted

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

12 votes
Accepted

Motivation for the definition of complex orientable cohomology theory

11 votes
Accepted

Lifting of map from $S^3$ to itself

10 votes
Accepted

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

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?

10 votes
Accepted

Are algebras of smooth functions formally smooth?

10 votes
Accepted

The number of polynomials on a finite group, II

9 votes
Accepted

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

9 votes

Is there a definition of reduced $E_\infty$ ring?

9 votes

Is the cohomology ring $H^*(BG,\mathbb{Z})$ generated by Euler classes?

9 votes
Accepted

($1$-)pullbacks of Kan complexes