2016/05/31 by Jun Zhang · 1 citation
Mathematics · #math.SG #math.AT #math.DS #msc:53D40
published as J. Symplectic Geom., Volume 17, Number 3 (2019), 857-927 · published version + a reference from S. Barannikov added
arxiv created 2021/02/08 · arxiv updated 2021/02/09
In this paper, we generalize the result from L. Polterovich and E. Shelukhin's paper stating that Hofer distance from time-dependent Hamiltonian diffeomorphism to the set of p-th power Hamiltonian diffeomorphism can be arbitrarily large to hold in the product structure Σg × M for any closed symplectic manifold M when p is sufficiently large and g ≥ 4. This implies that, on this product, Hofer distance can be arbitrarily large between time-dependent Hamiltonian diffeomorphism and autonomous Hamiltonian diffeomorphism.The basic tool we use is barcode and singular value decomposition that are developed in previous joint work with M. Usher, from which we borrow many proofs and modify them so that it can be adapted to the situation that filtered chain complex equipped with a group action.