bio | website | wwwmath.uni-muenster.de/… |
---|---|---|
location | Münster | |
age | 38 | |
visits | member for | 4 years |
seen | 10 hours ago | |
stats | profile views | 4,345 |
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 |