6 citations · 10 across the 7 of their papers we have counts for
7 papers
Gromov-Uhlenbeck Compactness
Max Lipyanskiy
We develop an analytic framework that combines the compactness theory of Gromov for J-holomorphic curves with that of Uhlenbeck for ASD connections. Compactness, regularity and rem…
Geometric Cycles in Floer Theory
Max Lipyanskiy
We construct a version of Hamiltonian Floer Homology based on the notion of a semi-infinite cycle. As an application, we provide a new proof for the existence of critical points of…
On Regularity of J-holomorphic Maps
Max Lipyanskiy
We provide a short proof that an and -holomorphic curve is in fact smooth. As an application, we deduce a removal of singularity theorem for curves of finite energy.
Geometric Homology
Max Lipyanskiy
The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the litera…
Geometric composition in quilted Floer theory
Yanki Lekili, Max Lipyanskiy
We prove that Floer cohomology of cyclic Lagrangian correspondences is invariant under transverse and embedded composition of Lagrangians under a general set of assumptions. In the…
Semi-Infinite Cycles in Floer Theory: Viterbo's Theorem
Max Lipyanskiy
This is the first of a series of papers on foundations of Floer theory. We give an axiomatic treatment of the geometric notion of a semi-infinite cycle. Using this notion, we intro…