17 citations · 50 across the 13 of their papers we have counts for
14 papers
Localization of Lagrangian Floer homology for -actions
Erkao Bao, Tyler Lawson, Cheuk Yu Mak
For an odd prime , we prove a Smith inequality over for exact Lagrangian Floer homology under a symplectic -action, assuming an equivariant stable n…
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,…
Equivariant Morse-Bott cohomology through stabilization
Erkao Bao, Robi Huq, Shengzhen Ning
For closed manifolds with compact Lie group actions, we study Austin-Braam's Morse-theoretic construction of Borel equivariant cohomology using the technique of stabilization. We s…
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…
Coherent orientations in symplectic field theory revisited
Erkao Bao
In symplectic field theory (SFT), the moduli spaces of -holomorphic curves can be oriented coherently (compatible with gluing). In this note, we correct the signs involved in th…
Immersed Lagrangian Floer cohomology via pearly trajectories
Garrett Alston, Erkao Bao
We define Lagrangian Floer cohomology over -coefficients by counting pearly trajectories for graded, exact Lagrangian immersions that satisfy certain positivity condit…
Equivariant neural networks and equivarification
Erkao Bao, Jingcheng Lu, Linqi Song +3
Equivariant neural networks are a class of neural networks designed to preserve symmetries inherent in the data. In this paper, we introduce a general method for modifying a neural…
Equivariant Lagrangian Floer cohomology via semi-global Kuranishi structures
Erkao Bao, Ko Honda
Using a simplified version of Kuranishi perturbation theory that we call semi-global Kuranishi structures, we give a definition of the equivariant Lagrangian Floer cohomology of a…
Semi-global Kuranishi charts and the definition of contact homology
Erkao Bao, Ko Honda
We define the contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. More precisely, given a contact manifold and some…
Definition of Cylindrical Contact Homology in dimension three
Erkao Bao, Ko Honda
In this paper we give a rigorous definition of cylindrical contact homology for contact -manifolds that admit nondegenerate contact forms with no contractible Reeb orbits, and s…
Exact, graded, immersed Lagrangians and Floer theory
Garrett Alston, Erkao Bao
We develop Lagrangian Floer Theory for exact, graded, immersed Lagrangians with clean self-intersection using Seidel's setup. A positivity assumption on the index of the self inter…
On Hofer Energy of J-holomorphic Curves for Asymptotically Cylindrical J
Erkao Bao
In this paper, we provide a bound for the generalized Hofer energy of punctured -holomorphic curves in almost complex manifolds with asymptotically cylindrical ends. As an appli…
Holomorphic curves at one point
Erkao Bao
Let M be a closed symplectic manifold with a compatible almost complex structure J. We prove that for a point p in M and E>0, if v is a non-constant J-holomorphic curve with symple…
On J-holomorphic curves in almost complex manifolds with asymptotically cylindrical ends
Erkao Bao
Symplectic Field Theory studies J-holomorphic curves in almost complex manifolds with cylindrical ends. One natural generalization is to replace 'cylindrical' by 'asymptotically cy…