The Mukai pairing, I: a categorical approach

By Andrei Căldăraru, Simon Willerton. 2007

132 citations recorded by the source corpus.

We study the Hochschild homology of smooth spaces, emphasizing the importance of a pairing which generalizes Mukai's pairing on the cohomology of K3 surfaces. We show that integral transforms between derived categories of spaces induce, functorially, linear maps on homology. Adjoint functors induce adjoint linear maps with respect to the Mukai pairing. We define a Chern character with values in Hochschild homology, and we discuss analogues of the Hirzebruch-Riemann-Roch theorem and the Cardy Condition from physics. This is done in the context of a 2-category which has spaces as its objects and integral kernels as its 1-morphisms.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/81bdb1f0ca0670e89884817b29402cc5b6d47a3a

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A category of kernels for equivariant factorizations and its implications for Hodge theory (2011, background): “of the Chern character map respects this decomposition. Proof. The ﬁrst part is as in the proof of Theorem 7.3 in see [Kuz09a] Theorem 7.3. The second part follows from Proposition 5 and Theorem 6 in [CW10]/Lemma 1.2.1 of [PV10a]. Proposition 10.6. For any v ∈HHi(T), β(v) = 0 if and only if hv,W(T)i”
Hirzebruch–Riemann–Roch‐type formula for DG algebras (2007, background): “Namely, it was explained in [9] (see also [11]) how to obtain a categorical version of the HRR theorem, similar to the one above, starting from the cohomology theory smooth spaces −→ graded vector spaces, X → HH•(X) (‘smooth spaces’ are understood in a broad sense: these are the usual schemes as wel”