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- W2184881284 abstract "This is a joint work with Masaki Kashiwara announced in [3]. On a complex manifold (X,OX), the Hochschild homology HH(OX) may be defined as the object RHomOX×X (ω ⊗−1 ∆ ,O∆) (see [1]), where ωX is the dualizing complex and ∆ is the diagonal. It is a powerful tool to construct characteristic classes of coherent modules and to get index theorems. Here, I will show how to adapt this formalism to a wide class of sheaves on a real manifold M . For that purpose, we have to work “microlocally”, that is, on the cotangent bundle T ∗M and to replace the functor RHom by the functor μhom, a variant of Sato’s microlocalization functor. Then HH(OX) is replaced by HH(kM ) = μhom(ω⊗−1 ∆ , k∆), where now k is a ring and ωM stands for the topological dualizing complex. To a so-called Hochschild kernel we associate its microlocal Euler class in HH(kM ), a class on T ∗M supported by the microsupport of the kernel. The main theorem asserts that this class is functorial with respect to the composition of kernels. This construction applies in particular to constructible sheaves on real manifolds and D-modules (or more generally, elliptic pairs) on complex manifolds giving a new approach to the Riemann-Roch or Atiyah-Singer theorems." @default.
- W2184881284 created "2016-06-24" @default.
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- W2184881284 date "2005-01-01" @default.
- W2184881284 modified "2023-09-27" @default.
- W2184881284 title "Hochschild homology and microlocal Euler classes" @default.
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