Equivariant Lagrangian Floer homology and Extended Field theory

25 January 2021
Guillem Cazassus
Given a compact Lie group G and a Hamiltonian G-manifold endowed with a pair of G-Lagrangians, we provide a construction for their equivariant Floer homology. Such groups have been defined previously by Hendricks, Lipshitz and Sarkar, and also by Daemi and Fukaya. A similar construction appeared independently in the work of Kim, Lau and Zheng. We will discuss an attempt to use such groups to construct topological field theories: these should be seen as 3-morphism spaces in the Hamiltonian 3-category, which should serve as a target for a field theory corresponding to Donaldson polynomials.

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  • Geometry and Analysis Seminar