5 papers
From Morse Trees to -Holomorphic Discs -- Rigid Y-Graphs
Erkao Bao, Ke Zhu
The correspondence between Morse flow trees and -holomorphic discs was established by Fukaya--Oh and Ekholm. We revisit this correspondence and present an alternative approach,…
Linearity and virtual poly-freeness of the fundamental group of plane curves of degree at most five
Shengkui Ye, Kejia Zhu
We prove that for any algebraic plane curve of degree at most , the fundamental group is linear and virtually polyfree. As a consequence, we…
Atypical generic directions in Teichmüller space
Matthew Gentry Durham, Chenxi Wu, Kejia Zhu
Motivated by geometrically capturing generic directions in Teichmüller space -- that is, tracking rays for random walks of the mapping class group -- we use work of Chaika--Masur-…
CAT(0) geometry of complex curve complements and families
Corey Bregman, Anatoly Libgober, Kejia Zhu
Motivated by the question of whether braid groups are CAT(0), we investigate the CAT(0) behavior of fundamental groups of plane curve complements and certain universal families. If…
Computable, obstructed Morse homology for clean intersections
Erkao Bao, Ke Zhu
In this paper, we develop a method to compute the Morse homology of a manifold when descending manifolds and ascending manifolds intersect cleanly, but not necessarily transversely…