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The Thom-Sebastiani theorem for the Euler characteristic of cyclic L-infinity algebras | Yunfeng Jiang
; | Date: |
24 Nov 2015 | Abstract: | Let $L$ be a cyclic $L_infty$-algebra of dimension $3$ with finite
dimensional cohomology only in dimension one and two. By transfer theorem there
exists a cyclic $L_infty$-algebra structure on the cohomology $H^*(L)$. The
inner product plus the higher products of the cyclic $L_infty$-algebra defines
a superpotential function $f$ on $H^1(L)$. We associate with an analytic Milnor
fiber for the formal function $f$ and define the Euler characteristic of $L$ is
to be the Euler characteristic of the ’etale cohomology of the analytic Milnor
fiber.
In this paper we prove a Thom-Sebastiani type formula for the Euler
characteristic of cyclic $L_infty$-algebras. As applications we prove the
Joyce-Song formulas about the Behrend function identities for semi-Schur
objects in the derived category of coherent sheaves over Calabi-Yau threefolds.
A motivic Thom-Sebastiani type formula and a conjectural motivic Joyce-Song
formulas for the motivic Milnor fiber of cyclic $L_infty$-algebras are also
discussed. | Source: | arXiv, 1511.7912 | Services: | Forum | Review | PDF | Favorites |
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