BV bialgebra structures in Floer theory and string topology

Abstract

We derive the notions of BV unital infinitesimal bialgebra and BV Frobenius algebra from the topology of suitable compactifications of moduli spaces of decorated genus 0 curves. We construct these structures respectively on reduced symplectic homology and Rabinowitz Floer homology. As an application, we construct these structures in nonequivariant string topology. We also show how the Lie bialgebra structure in equivariant string topology, and more generally on $S^1$-equivariant symplectic homology, is obtained as a formal consequence.

reformulated some results in terms of Tate vector spaces (also added new appendix recalling basic theory of Tate vector spaces), small changes in exposition in response to reader comments