65 citations · 91 across the 20 of their papers we have counts for
10 papers · 1 filter
Searching for -holomorphic curves via machine: first steps
James Rowan, Yuan Yao
We assemble numerical algorithms to search for -holomorphic curves in symplectic manifolds. Each algorithm employs several different numerical techniques, each technique address…
Fixed Point Floer Cohomology of Dehn Twists I: Splitting Formulas
Maxim Jeffs, Yuan Yao, Ziwen Zhao
This paper is the first in a series following on our earlier work [arXiv:2205.14516, arXiv:2307.08180] studying the pair-of-pants product on fixed point Floer cohomology. In [arXiv…
An Invitation to Obstruction Bundle Gluing Through Morse Flow Lines
Ipsita Datta, Yuan Yao
We adapt "Obstruction Bundle Gluing (OBG)" techniques from Hutchings and Taubes (arxiv: 0701300, 0705.2074) to Morse theory. We consider Morse function-metric pairs with gradient f…
Anchored symplectic embeddings
Michael Hutchings, Agniva Roy, Morgan Weiler +1
Given two four-dimensional symplectic manifolds, together with knots in their boundaries, we define an ``anchored symplectic embedding'' to be a symplectic embedding, together with…
On Symplectic Packing Problems in Higher Dimensions
Kyler Siegel, Yuan Yao
Let denote the closed -dimensional symplectic ball of area , and let be a closed symplectic surface of genus and area . We prove that there is a…
Fixed point Floer cohomology and closed-string mirror symmetry for nodal curves
Maxim Jeffs, Yuan Yao, Ziwen Zhao
We show that for singular hypersurfaces, a version of their genus-zero Gromov-Witten theory may be described in terms of a direct limit of fixed point Floer cohomology groups, a co…
Legendrian embedded contact homology
Julian Chaidez, Oliver Edtmair, Luya Wang +2
We give a construction of embedded contact homology (ECH) for a contact -manifold with convex sutured boundary and a pair of Legendrians and contained in $\parti…
Computing Embedded Contact Homology in Morse-Bott Settings
Yuan Yao
Given a contact three manifold with a nondegenerate contact form , and an almost complex structure compatible with , its embedded contact homology is defin…
From Cascades to -holomorphic Curves and Back
Yuan Yao
This paper develops the analysis needed to set up a Morse-Bott version of embedded contact homology (ECH) of a contact three-manifold in certain cases. In particular we establish a…
Product and Coproduct on Fixed Point Floer Homology of Positive Dehn Twists
Yuan Yao, Ziwen Zhao
We compute the product and coproduct structures on the fixed point Floer homology of iterations on the single Dehn twist, subject to some mild topological restrictions. We show tha…