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Categorical Enumerative Invariants, I: String vertices
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Categorical Enumerative Invariants, I: String vertices
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We define combinatorial counterparts to the geometric string vertices of Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the moduli spaces of curves. Our combinatorial vertices contain the same information as the geometric ones, are effectively computable, and act on the Hochschild chains of a cyclic $A_\infty$-algebra. This is the first in a series of two papers where we define enumerative invariants associated to a pair consisting of a cyclic $A_\infty$-algebra and a splitting of the Hodge filtration on its cyclic homology. These invariants conjecturally generalize the Gromov-Witten and Fan-Jarvis-Ruan-Witten invariants from symplectic geometry, and the Bershadsky-Cecotti-Ooguri-Vafa invariants from holomorphic geometry.
Forward citations
Cited by 2 Pith papers
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B-model Categorical Enumerative Invariants and holomorphic anomaly equations
B-model CEI on Calabi-Yau 3-folds satisfy holomorphic anomaly equations after proving dilaton/string/divisor analogs and applying Givental quantization.
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Open-closed Deligne-Mumford field theories: geometric foundations
Constructs global Kuranishi charts for pseudo-holomorphic maps with boundary on Lagrangians of arbitrary genus and builds geometric foundations for compatible chain-level operations in open-closed DM field theories.
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