User Oscar Randal-Williams

58 votes

Examples where it's useful to know that a mathematical object belongs to some family of objects

answered Sep 1, 2011 at 13:10

37 votes

Accepted

All fiber bundles over $S^2$ extendable to $\mathbb{C}P^\infty$?

answered Oct 21, 2016 at 10:22

34 votes

Manifold embedded in $R^{n+1}$ with a submanifold that doesn't embed in $R^n$

answered Nov 8, 2016 at 12:56

32 votes

Accepted

Fundamental group of a topological pullback

answered May 30, 2013 at 14:03

31 votes

Does a "Chern character" exist for any generalized cohomology theory?

answered Jun 23, 2010 at 8:53

26 votes

Accepted

Mumford conjecture: Heuristic reasons? Generalizations? ... Algebraic geometry approaches?

answered Jan 10, 2010 at 15:44

26 votes

Accepted

Homology theory represented by Madsen-Tillmann spectra

answered Aug 25, 2014 at 9:48

26 votes

Accepted

Approximation of homeomorphism by diffeomorphism

answered Dec 18, 2019 at 8:03

23 votes

Accepted

Are homology spheres stably parallelisable?

answered Jun 16, 2016 at 20:31

23 votes

Accepted

Square root of the determinant line

answered Oct 10, 2017 at 11:23

22 votes

Accepted

Group completion theorem

answered Mar 4, 2010 at 20:40

20 votes

Can one give an immersion of exotic sphere $S^7$ in a standard sphere $S^8$ of radius $1$?

answered Jun 26, 2013 at 7:28

20 votes

Accepted

Uniqueness of compactification of an end of a manifold

answered Nov 23, 2011 at 17:25

19 votes

Accepted

Is the cohomology ring of a finite group computable?

answered May 9, 2018 at 6:43

19 votes

Accepted

Product-like structures on spheres

answered Nov 28, 2015 at 20:16

18 votes

Accepted

Is every ''group-completion'' map an acyclic map?

answered Oct 16, 2012 at 16:57

18 votes

Betti numbers of moduli spaces of smooth Riemann surfaces

answered Sep 16, 2010 at 13:32

18 votes

Accepted

Loop spaces and infinite braids

answered Oct 30, 2010 at 20:36

18 votes

Accepted

Are the associative grassmannian and the quaternionic projective plane diffeomorphic?

answered Apr 13, 2011 at 8:25

17 votes

Accepted

K(F_1) = sphere spectrum?

answered Oct 21, 2009 at 11:21

17 votes

Is the counit of geometric realization a Serre fibration?

answered Jun 24, 2013 at 13:35

17 votes

Accepted

Which stable homotopy groups are represented by parallelizable manifolds?

answered Jun 26, 2020 at 20:20

16 votes

Accepted

Homotopy groups of Diff(X) and Homeo(X)

answered Oct 7, 2020 at 12:37

16 votes

Pin$^+$ and Pin$^−$ structure for manifolds in any dimensions

answered Dec 23, 2016 at 7:54

16 votes

Accepted

Are all unstable homotopy groups of $U(n)$ torsion?

answered Nov 12, 2014 at 7:50

16 votes

Accepted

Topological Grothendieck Construction

answered Mar 6, 2015 at 12:53

15 votes

Accepted

Why is the first chern class of a line bundle $c_1(L) = 1-L$ in complex K-theory?

answered Mar 14, 2015 at 23:56

15 votes

Accepted

Can the standard map $\Sigma \Omega X \to X$ be a homotopy equivalence?

answered Sep 22, 2015 at 9:35

15 votes

Accepted

Non-realizability of $\mathbb{Q}$ as a cohomology group

answered Sep 23, 2015 at 17:31

15 votes

Accepted

Computation of stable homotopy groups of $RP^2$

answered Nov 20, 2012 at 18:40

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157 Answers

Examples where it's useful to know that a mathematical object belongs to some family of objects

All fiber bundles over $S^2$ extendable to $\mathbb{C}P^\infty$?

Manifold embedded in $R^{n+1}$ with a submanifold that doesn't embed in $R^n$

Fundamental group of a topological pullback

Does a "Chern character" exist for any generalized cohomology theory?

Mumford conjecture: Heuristic reasons? Generalizations? ... Algebraic geometry approaches?

Homology theory represented by Madsen-Tillmann spectra

Approximation of homeomorphism by diffeomorphism

Are homology spheres stably parallelisable?

Square root of the determinant line

Group completion theorem

Can one give an immersion of exotic sphere $S^7$ in a standard sphere $S^8$ of radius $1$?

Uniqueness of compactification of an end of a manifold

Is the cohomology ring of a finite group computable?

Product-like structures on spheres

Is every ''group-completion'' map an acyclic map?

Betti numbers of moduli spaces of smooth Riemann surfaces

Loop spaces and infinite braids

Are the associative grassmannian and the quaternionic projective plane diffeomorphic?

K(F_1) = sphere spectrum?

Is the counit of geometric realization a Serre fibration?

Which stable homotopy groups are represented by parallelizable manifolds?

Homotopy groups of Diff(X) and Homeo(X)

Pin$^+$ and Pin$^−$ structure for manifolds in any dimensions

Are all unstable homotopy groups of $U(n)$ torsion?

Topological Grothendieck Construction

Why is the first chern class of a line bundle $c_1(L) = 1-L$ in complex K-theory?

Can the standard map $\Sigma \Omega X \to X$ be a homotopy equivalence?

Non-realizability of $\mathbb{Q}$ as a cohomology group

Computation of stable homotopy groups of $RP^2$