12,345 reputation
3970
bio website wwwmath.uni-muenster.de/…
location Münster
age 38
visits member for 3 years, 10 months
seen Jul 31 at 8:47

I am a mathematician based in Münster, Germany. A fellow MO user once described me as a ''very homotopy-theoretic geometric topologist'' and I largely approve this description.


Jul
16
awarded  Enlightened
Jul
16
awarded  Nice Answer
Jul
16
revised Homotopy spheres with vanishing and non-vanishing $\alpha$-invariant
added 7 characters in body
Jul
16
answered Norms on Clifford algebra (C^* norm)
Jul
11
answered Euler Class of a vector field
Jul
11
comment Euler Class of a vector field
@Henry T. Horton: you can only take the orthogonal complement if the vector field does not have a zero.
Jul
2
awarded  Curious
Jun
25
comment Question about the fundamental group of rational homology 3-spheres
If I am not mistaken (!), this shows, together with the poincare conjecture, that $M$ is a connected sum of two lens spaces. So unless $M$ is a sum of lens spaces, it has $\pi_2 (M) =0$.
Jun
25
comment Question about the fundamental group of rational homology 3-spheres
I do not know if that helps, but here is a remark. Assume that $M$ is an oriented rational homology sphere such that $\pi_1 (M)$ requires 2 generators. If $\pi_2 (M) \neq 0$, then $M$ contains an embedded $S^2$ which is nontrivial in homotopy (by the sphere theorem). This sphere must be two-sided, and so by cutting $M$ along the sphere, you write $M$ in a nontrivial way as the connected sum of two manifolds; and both of them are rational homology spheres, and none is simply connected (by the Poincare conjecture). By Grushko's theorem, the fundamental groups of both pieces are cyclic.
Jun
17
revised Homotopy spheres with vanishing and non-vanishing $\alpha$-invariant
added 156 characters in body
Jun
16
answered Homotopy spheres with vanishing and non-vanishing $\alpha$-invariant
May
28
comment Construction of a Bott manifold
The spin bordism group of 8-dimensional manifolds is $Z \oplus Z$, detected by the $\hat{A}$-genus and the signature. A basis is given by a Bott manifold $B$ and $HP^2$. The K3-surface K has $\hat{A} (K^2) =4$ and $\sign (K^2)=16^2$. Therefore $[K^2] = 16^2 [HP^2]+ 4 [B]$, and this yields Laures formula (note that $[K^2]$ is divisible by 4).
May
28
answered Construction of a Bott manifold
May
13
awarded  Nice Answer
May
1
revised Signature of compact oriented 4-manifold
edited body
Apr
25
awarded  Nice Answer
Apr
25
revised When does a cohomology class induce an isomorphism between homotopy groups?
added 1093 characters in body
Apr
24
answered When does a cohomology class induce an isomorphism between homotopy groups?
Apr
9
awarded  Enlightened
Apr
9
awarded  Nice Answer