3 papers
math.GT2023
On the Whitney disks in Heegaard Floer homology theory
Shengwen Xie, Xuezhi Zhao
The Whitney disks play a central role in defining Heegaard Floer homology of a -dimensional manifold. We use Nielsen theory to a simple criterion to the existence of Whitney dis…
math.AT2023
Persistence of sub-chain groups
Fang Sun, Shengwen Xie, Xuezhi Zhao
In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a mor…
math.DS2014
Density of the homotopy minimal periods of maps on infra-solvmanifolds
Jong Bum Lee, Xuezhi Zhao
We study the homotopical minimal periods for maps on infra-solvmanifolds of type (R) using the density of the homotopical minimal period set in the natural numbers. This extends th…