2013/10/31 by Peter Albers, Doris Hein · 1 citation
Mathematics · #math.DG #math.SG
paper · pdf · doi:10.1142/s1793525316500102
published as Journal of Topology and Analysis, (2016), 243 - 272 · 25 pages, 1 figure, appeared online in Journal of Topology and Analysis
arxiv created 2015/07/17 · arxiv updated 2016/03/22
The main goal of this paper is to give a unified treatment to many known cuplength estimates. As the base case, we prove that for C0-perturbations of a function which is Morse-Bott along a closed submanifold, the number of critical points is bounded below in terms of the cuplength of that critical submanifold. As we work with rather general assumptions the proof also applies in a variety of Floer settings. For example, this proves lower bounds for the number of fixed points of Hamiltonian diffeomorphisms, Hamiltonian chords for Lagrangian submanifolds, translated points of contactomorphisms, and solutions to a Dirac-type equation.