6 citations · 16 across the 18 of their papers we have counts for
18 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 a…
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…
A note on complex hyperbolic lattices and strict hyperbolization
Kejia Zhu
We study the connection between the fundamental groups of complex hyperbolic manifolds and those of spaces arising from the (relative) strict hyperbolization process due to Charney…
Relatively geometric actions of Kähler groups on CAT(0) cube complexes
Corey Bregman, Daniel Groves, Kejia Zhu
We prove that for , a non-uniform lattice in does not admit a relatively geometric action on a cube complex, in the sense of Einstein an…
Conditions on the monodromy for a surface group extension to be CAT(0)
Kejia Zhu
In order to determine when surface-by-surface bundles are non-positively curved, Llosa Isenrich and Py give a necessary condition: given a surface-by-surface group with infinit…
Bounds on degrees of covers with injective monodromy in iterated Kodaira Fibrations
Kejia Zhu
Let be an -dimensional iterated Kodaira fibration with fiber of genus and injective monodromy. Llosa Isenrich and Py proved that we can pass to a finite index sub…
Solvability of Dirac type equations
Qingchun Ji, Ke Zhu
This paper develops a weighted -method for the (half) Dirac equation. For Dirac bundles over closed Riemann surfaces, we give a sufficient condition for the solvability of the…
High-jet relations of the heat kernel embedding map and applications
Ke Zhu
For any compact Riemannian manifold and its heat kernel embedding map from M into constructed in [BBG], we study the higher derivatives of with respec…
Isometric embeddings via heat kernel
Xiaowei Wang, Ke Zhu
For any n-dimensional compact Riemannian manifold (M,g), we construct a canonical t-family of isometric embeddings I_{t}: M->R^{q(t)}, with t>0 sufficiently small and q(t)>>t^{-n/2…
Instantons in G2 manifolds from J-holomorphic curves in coassociative submanifolds
Naichung Conan Leung, Xiaowei Wang, Ke Zhu
In G2 manifolds, 3-dimensional associative submanifolds (instantons) play a role similar to J-holomorphic curves in symplectic geometry. In [21], instantons in G2 manifolds were co…
Thin instantons in G_2-manifolds and Seiberg-Witten invariants
Naichung Conan Leung, Xiaowei Wang, Ke Zhu
For two nearby disjoint coassociative submanifolds C and C' in a G_2-manifold, we construct thin instantons with boundaries lying on C and C' from regular J-holomorphic curves in C…
Partial collapsing degeneration of Floer trajectories and adiabatic gluing
Yong-Geun Oh, Ke Zhu
We study partial collapsing degeneration of Hamiltonian-perturbed Floer trajectories for an adiabatic -family and its reversal adiabatic gluing, as the prototype of th…
Moduli Spaces of -holomorphic Curves with General Jet Constraints
Ke Zhu
In this paper, we prove that the tagent map of the holomorphic - jet evaluation from the mapping space to holomorphic -jet bundle, when restricted on the universa…
Embedding property of -holomorphic curves in Calabi-Yau manifolds for generic
Yong-Geun Oh, Ke Zhu
In this paper, we prove that for a generic choice of tame (or compatible) almost complex structures on a symplectic manifold with and with its first Che…
Floer trajectories with immersed nodes and scale-dependent gluing
Yong-Geun Oh, Ke Zhu
We define an enhanced compactification of Floer trajectories under Morse background using the adiabatic degeneration and the scale-dependent gluing techniques. The compactification…