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Though the Atiyah-Singer index theorem holds for pseudodifferential operators, all the applications of the index theorem I know of only need it for Dirac-type operators. I know that pseudodifferential ...

Hi, I'm currently trying to understand the Atiyah-Singer index theorem and its proof as presented in the book "Spin Geometry" by Lawson and Michelsohn. I do not understand why the analytic index map ...

In the paper "Local Index Formula in Noncommutative Geometry" Connes and Moscovici build the spectral triple $(A,H,D)$ where $A=C^{\infty}_c(P) \rtimes \Gamma$ where $\Gamma$ is an arbitrary subgroup ...

I am reading the thesis of Chris Kottke (https://dspace.mit.edu/bitstream/handle/1721.1/60193/681923895-MIT.pdf) and I would need some help to try to understand intuitively why he makes the choice of ...