相关论文: Bordered Floer homology and incompressible surface…

We compute the Ozsvath-Szabo Floer homologies HF^{+-} and HF-hat for three-manifolds obtained by integer surgery on a two-bridge knot.

The perturbation expansion for a general class of many-fermion systems with a non-nested, non-spherical Fermi surface is renormalized to all orders. In the limit as the infrared cutoff is removed, the counterterms converge to a finite limit…

Viewing the BRAID invariant as a generator of link Floer homology we generalise work of Baldwin-Vela-Vick to obtain rank bounds on the next to top grading of knot Floer homology. These allow us to classify links with knot Floer homology of…

Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow for instance quadratically in the fibers outside of a compact set,…

We show that the link cobordism maps defined by the author are graded and satisfy a grading change formula. Using the grading change formula, we prove a new bound for $\Upsilon_K(t)$ for knot cobordisms in negative definite 4-manifolds. As…

Starting from a Heegaard splitting of a three-manifold, we use Lagrangian Floer homology to construct a three-manifold invariant, in the form of a relatively Z/8-graded abelian group. Our motivation is to have a well-defined symplectic side…

We apply Heegaard Floer homology to study deformations of singularities of plane algebraic curves. Our main result provides an obstruction to the existence of a deformation between two singularities. Generalizations include the case of…

We prove new adjunction inequalities for embedded surfaces in four-manifolds with non-negative self-intersection number by using the Donaldson invariants. These formulas are completely analogous to the ones obtained by Ozsv\'ath and Szab\'o…

We study the existence of incompressible embeddings of surfaces into the genus two handlebody. We show that for every compact surface with boundary, orientable or not, there is an incompressible embedding of the surface into the genus two…

We develop the 2-representation theory of the odd one-dimensional super Lie algebra $gl(1|1)^+$ and show it controls the Heegaard-Floer theory of surfaces of Lipshitz, Ozsv\'ath and Thurston. Our main tool is the construction of a tensor…

We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…

Extending ideas of Hedden-Ni, we show that the module structure on Khovanov homology detects split links. We also prove an analogue for untwisted Heegaard Floer homology of the branched double cover. Technical results proved along the way…

We prove Furuta-type bounds for the intersection forms of spin cobordisms between homology 3-spheres. The bounds are in terms of a new numerical invariant of homology spheres, obtained from Pin(2)-equivariant Seiberg-Witten Floer K-theory.…

We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in Z/2). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the…

In this paper, we show that the pointwise finite-dimensional two-parameter persistence module $\mathbb{HF}_*^{(\bullet,\bullet]}$, defined in terms of interlevel filtered Floer homology, is rectangle-decomposable. This allows for the…

This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the…

We give new obstructions to the module structures arising in Heegaard Floer homology. As a corollary, we characterize the possible modules arising as the Heegaard Floer homology of an integer homology sphere with one-dimensional reduced…

Let $Y_1$ be a closed, oriented 3-manifold and $\Sigma$ denote a non-separating closed, orientable surface in $Y_1$ which consists of two connected components of the same genus. By cutting $Y_1$ along $\Sigma$ and re-gluing it using an…

This note explores two questions: (1) Which bigraded groups arise as the knot Floer homology of a knot in the three-sphere? (2) Given a knot, how many distinct knots share its Floer homology? Regarding the first, we show there exist…

We develop a version of Seiberg--Witten Floer cohomology/homotopy type for a spin$^c$ 4-manifold with boundary and with an involution which reverses the spin$^c$ structure, as well as a version of Floer cohomology/homotopy type for oriented…