Wrapped Floer homology of real Lagrangians and volume growth of fibered twists

Abstract

In this thesis we study wrapped Floer homology of real Lagrangians and its applications. We investigate an entropy-type invariant, called the slow volume growth, in the component of the group of symplectomorphisms which contain fibered twists. We give a uniform lower bound of the growth using wrapped Floer homology. We apply our results to fibered twists coming from complements of a symplectic hypersurface in a real symplectic manifold. They admit so-called real Lagrangians, and we can explicitly compute wrapped Floer homology of them using a Morse-Bott spectral sequence. We also introduce equivariant wrapped Floer homology following ideas proposed by Seidel-Smith. We then establish a Leray-Serre spectral sequence for equivariant wrapped Floer homology.