12,515 reputation
4072
bio website wwwmath.uni-muenster.de/…
location Münster
age 38
visits member for 4 years
seen 10 hours ago

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.


Oct
15
comment Has uniform ellipticity implications on the spectrum?
I forgot to mention that the Dirac operator is uniformly elliptic. It seems that the conditions in my post concern the order 0 part, while uniform ellipticity concerns the order 1 part.
Oct
15
revised Has uniform ellipticity implications on the spectrum?
added 254 characters in body
Oct
15
revised Has uniform ellipticity implications on the spectrum?
added 254 characters in body
Oct
15
answered Has uniform ellipticity implications on the spectrum?
Oct
14
answered Fundamental class in K-theory and orientability
Oct
10
awarded  Yearling
Sep
30
awarded  Explainer
Sep
8
comment Elliptic operator are unbounded
This is proven in full detail in section 1.6 of the book by Gilkey that you mentioned.
Sep
1
awarded  Nice Answer
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