bio | website | wwwmath.uni-muenster.de/… |
---|---|---|
location | Münster | |
age | 38 | |
visits | member for | 4 years, 3 months |
seen | 2 days ago | |
stats | profile views | 4,518 |
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.
Jan 7 |
answered | The periodic values in Bott periodicity |
Jan 7 |
answered | How to show the square root function of a positive semidefinite matrix is differentiable? |
Jan 5 |
revised |
Homotopy spheres with vanishing and non-vanishing $\alpha$-invariant
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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?
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