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29 March 2024
 
  » arxiv » 1511.7912

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The Thom-Sebastiani theorem for the Euler characteristic of cyclic L-infinity algebras
Yunfeng Jiang ;
Date 24 Nov 2015
AbstractLet $L$ 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
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