Abstract
We consider a smooth submanifold $N$ with a smooth boundary in an ambient closed manifold $M$ and assign a spectral invariant $c(\alpha,H)$ to every singular homological class $\alpha\in H_*(N)$ and a Hamiltonian $H$ defined on the cotangent bundle $T^*M$. We also derive certain properties of spectral numbers, for example we prove that spectral invariants $c_\pm(H,N)$ associated to the whole Floer homology $HF_*(H,N:M)$ of the submanifold $N$, are the limits of decreasing nested family of open sets.
Citation
Jelena Katić. Darko Milinković. Jovana Nikolić. "Spectral numbers and manifolds with boundary." Topol. Methods Nonlinear Anal. 55 (2) 617 - 653, 2020. https://doi.org/10.12775/TMNA.2019.108