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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2025 Volume 21, 030, 16 pp. (Mi sigma2147)

Sign Convention for $A_{\infty}$-Operations in Bott–Morse Case

Kaoru Ono

Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

Abstract: We describe the sign and orientation issue appearing the filtered $A_{\infty}$-formulae in Lagrangian Floer theory using de Rham model in Bott–Morse setting. After giving the definition of filtered $A_{\infty}$-operations in a Fukaya category, we verify the filtered $A_{\infty}$-formulae.

Keywords: filtered $A_{\infty}$-operation, Kuranishi structure, bordered stable map.

MSC: 53D40, 53D37, 58A99

Received: July 14, 2024; in final form March 3, 2025; Published online April 29, 2025

Language: English

DOI: 10.3842/SIGMA.2025.030



© Steklov Math. Inst. of RAS, 2025