12,725 reputation
4274
bio website wwwmath.uni-muenster.de/…
location Münster
age 38
visits member for 4 years, 2 months
seen 16 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.


Dec
13
answered Equation for non-invertible elements in Clifford algebras
Dec
2
comment Local index formula for >ungraded< elliptic operators
Typically, you would replace the operator $P$ by $P \oplus P^{\ast}: E \oplus F \to E \oplus F$. This is graded, and the index (in the graded sense) is the usual index. An ungraded operator has an index in $K^1$, but only if it is self-adjoint.
Nov
26
comment Is true that $\left[\frac{\hat{A}(\mathbb HP^m)} { \hat{M}(\mathbb HP^m) }\right]_{4m} = 0$?
I think I agree. What I did not realize was that $F$ is obtained from $(x/2)/\sinh(x/2)$ by a simple scaling in the argument. In that case, the components of the multiplicative seqeunce of $F$ are obtained from the components of the A-hat-genus by multiplication with constants.
Nov
24
awarded  Favorite Question
Nov
20
awarded  Enlightened
Nov
20
awarded  Nice Answer
Nov
20
comment Is true that $\left[\frac{\hat{A}(\mathbb HP^m)} { \hat{M}(\mathbb HP^m) }\right]_{4m} = 0$?
yes, the formula has a typo in it.
Nov
19
comment Is true that $\left[\frac{\hat{A}(\mathbb HP^m)} { \hat{M}(\mathbb HP^m) }\right]_{4m} = 0$?
@Juan: I could have guessed. I came across the paper, but did not understand what is going on. Can you tell me what the index theoretic significance of the Mayer class is?
Nov
19
answered Is true that $\left[\frac{\hat{A}(\mathbb HP^m)} { \hat{M}(\mathbb HP^m) }\right]_{4m} = 0$?
Nov
19
comment Is true that $\left[\frac{\hat{A}(\mathbb HP^m)} { \hat{M}(\mathbb HP^m) }\right]_{4m} = 0$?
And where does the Mayer class come from? I am just curious.
Nov
19
comment Is true that $\left[\frac{\hat{A}(\mathbb HP^m)} { \hat{M}(\mathbb HP^m) }\right]_{4m} = 0$?
What is the Mayer class? I have never heard about it.
Oct
30
comment What are the “correct” conventions for defining Clifford algebras?
@Qiaochu: then I recommend to take the tangent bundle. Another situation where one (e.g. me this week) has to be more careful is when you scale metrics by positive functions $f:M \to R$.
Oct
29
comment What are the “correct” conventions for defining Clifford algebras?
It is almost totally irrelevant whether you take tangent or cotangent bundles; all the theory is for Riemann manifolds, where both are naturally isomorphic.
Oct
29
comment What are the “correct” conventions for defining Clifford algebras?
I always take $\epsilon =-1$; because this turns the Dirac operator into a formally self-adjoint one and the Laplacian into a nonnegative operator. Everything else becomes extremely unnatural when doing analysis of elliptic operators.
Oct
29
awarded  Nice Answer
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