Spectral Invariants in Lagrangian Floer homology of open subset

TL;DR

This paper introduces spectral invariants for Floer homology of open subsets in cotangent bundles, establishing their algebraic properties, continuity, and relation to periodic orbit invariants.

Contribution

It defines spectral invariants for Floer homology of open subsets and proves their algebraic, continuity, and comparison properties, extending prior work.

Findings

Defined spectral invariants for Floer homology of open subsets.

Proved the triangle inequality for these invariants.

Established continuity and comparison with periodic orbit invariants.

Abstract

We define and investigate spectral invariants for Floer homology $HF(H,U:M)$ of an open subset $U\subset M$ in $T^*M$, defined by Kasturirangan and Oh as a direct limit of Floer homologies of approximations. We define a module structure product on $HF(H,U:M)$ and prove the triangle inequality for invariants with respect to this product. We also prove the continuity of these invariants and compare them with spectral invariants for periodic orbits case in $T^*M$.