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Homology concordance and knot Floer homology
We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer...
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Loop coproduct in Morse and Floer homology
By a well-known theorem of Viterbo, the symplectic homology of the cotangent bundle of a closed manifold is isomorphic to the homology of its loop...
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Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology
Continuing our previous work in [23], we effectively compute connected Heegaard Floer homologies of two families of Brieskorn spheres realized as...
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Knot Floer homology and relative adjunction inequalities
We establish inequalities that constrain the genera of smooth cobordisms between knots in 4-dimensional cobordisms. These “relative adjunction...
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Toward Computational Morse–Floer Homology: Forcing Results for Connecting Orbits by Computing Relative Indices of Critical Points
To make progress toward better computability of Morse–Floer homology and thus enhance the applicability of Floer theory, it is essential to have...
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Floer Homology: From Generalized Morse–Smale Dynamical Systems to Forman’s Combinatorial Vector Fields
We construct a Floer type boundary operator for generalised Morse–Smale dynamical systems on compact smooth manifolds by counting the number of...
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Knot Floer homology of satellite knots with (1, 1) patterns
For pattern knots admitting genus-one doubly pointed bordered Heegaard diagrams, we give an immersed-curve approach to compute the knot Floer chain...
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Decomposing sutured monopole and instanton Floer homologies
In this paper, we generalize the work of the second author in Li (Direct systems and the knot monopole Floer homology, 2019.
ar**v:1901.06679 ...
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A Note on Partial Quasi-Morphisms and Products in Lagrangian Floer Homology in Cotangent Bundles
We define partial quasi-morphisms on the group of Hamiltonian diffeomorphisms of the cotangent bundle using the spectral invariants in Lagrangian...
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Seiberg–Witten Floer spectra and contact structures
In this article, the author defines an invariant of rational homology 3-spheres equipped with a contact structure as an element of a cohomotopy set...
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The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II
This paper is the sequel to (Colin et al. in Publ. Math. Inst. Hautes Études Sci.,
2024 ), and is devoted to proving some of the technical parts of... -
Partial Collapsing Degeneration of Floer Trajectories and Adiabatic Gluing
In the present paper, we study partial collapsing degeneration of Hamiltonian-perturbed Floer trajectories for an adiabatic ε -family and its reversal...
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A Note on Knot Floer Homology and Fixed Points of Monodromy
Using an argument of Baldwin–Hu–Sivek, we prove that if K is a hyperbolic fibered knot with fiber F in a closed, oriented 3-manifold Y , and
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Critical Points of Potential Functions and Floer Cohomology
In this chapter, with the analysis of one-point open Gromov–Witten invariants given in the previous section at our disposal, we develop the critical...
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