All Questions

I would like to ask a question on the bibliography of the index theorems on manifold with boundary. Before my bibliographical research my understanding of the field was that for manifold with boundary,...

The eta function of a differential operator was used by Atiyah, Patodi and Singer to derive their famous index theorem, and is given by $$ \eta(s)=\sum_{\lambda\neq 0}(\mathrm{sign}\lambda)|\lambda|^...

Let $D$ be a differential operator acting between the spaces of smooth sections of two vector bundles $E,F$ over compact manifold $M$. If $M$ is not simply connected one can construct the universal ...

When I read about Atiyah Singer index theorem I met the following example: let $M$ is (orientable closed smooth) Riemannian manifold and consider Hodge-de Rham Dirac operator defined by $d+d^*$ (...

Edit According to the comment of Alex Degtyarev, I deleted the last part of the previous version. Let $E$ be a real vector space. The complex valued $k$- tensors on $E$ is denoted by $L_{\mathbb{C}}^{...

Let $\pi:E\to M$ be a smooth vector bundle over a smooth manifold, with $\text{rank}(E)=\text{dim}(M)$. For a section $\sigma$ of $E$ with a zero at $p\in M$, define the degree of the zero at $p$ to ...