Related papers: Higher type adjunction inequalities for Donaldson …
To every compact oriented surface that is composed entirely out of 2-dimensional 0- and 1-handles, we construct a dg category using structures arising in Khovanov homology. These dg categories form part of the 2-dimensional layer (a.k.a.…
In this article we complete the proof---for a broad class of four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear…
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 provide an explicit formula for localizing $A^1$-homotopy invariants of topological Fukaya categories of marked surfaces. Following a proposal of Kontsevich, this differential $\mathbb Z$-graded category is defined as global sections of…
Upsilon is a homomorphism on the smooth concordance group of knots defined by Ozsv\'{a}th, Stipsicz and Szab\'{o}. In this paper, we define a generalization of upsilon for a family of embedded graphs in rational homolog spheres. We show…
The Floer cohomology of a symplectic automorphism and that of its square are related by the pair-of-pants product. For exact symplectic automorphisms, we introduce an equivariant version of that product, and use it to prove a Smith-type…
We construct cobordism maps for the \textit{minus} version of instanton knot homology associated to a \textit{specially decorated} knot cobordisms of arbitrary genus between two null-homologous knots in closed oriented $3$-manifolds. As an…
In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The…
To a region $C$ of the plane satisfying a suitable convexity condition we associate a knot concordance invariant $\Upsilon^C$. For appropriate choices of the domain this construction gives back some known knot Floer concordance invariants…
Using the Gordon-Litherland pairing, one can define invariants (signature, nullity, determinant) for ${\mathbb Z}/2$ null-homologous links in thickened surfaces. In this paper, we study the concordance properties of these invariants. For…
Let $X$ and $X'$ be nonsingular projective $3$-folds related by a flop of a disjoint union of $(-2)$-curves. We prove a flop formula relating the Donaldson-Thomas invariants of $X$ to those of $X'$, which implies some simple relations among…
Using instanton homology with coefficients in $Z/2$ we construct a homomorphism $q_2$ from the homology cobordism group in dimension 3 to the integers which is not a rational linear combination of the instanton $h$--invariant and the…
In 1983, Donaldson shocked the topology world by using instantons from physics to prove new theorems about four-dimensional manifolds, and he developed new topological invariants. In 1988, Witten showed how these invariants could be…
Seidel-Smith and Hendricks used equivariant Floer cohomology to define some spectral sequences from symplectic Khovanov homology and Heegaard Floer homology. These spectral sequences give rise to Smith-type inequalities. Similar-looking…
We construct a new autoequivalence of the derived category of the Hilbert scheme of n points on a K3 surface, and of the variety of lines on a smooth cubic 4-fold. For Hilb^2 and the variety of lines, we use the theory of spherical…
We define an invariant of three-manifolds with an involution with non-empty fixed point set of codimension $2$; in particular, this applies to double branched covers over knots. Our construction gives the Heegaard Floer analogue of Li's…
We give constraints on smooth families of 4-manifolds with boundary using Manolescu's Seiberg-Witten Floer stable homotopy type, provided that the fiberwise restrictions of the families to the boundaries are trivial families of 3-manifolds.…
In this paper we show that even in the case of simply connected minimal algebraic surfaces of general type, deformation and differentiable equivalence do not coincide. Exhibiting several simple families of surfaces which are not deformation…
An obstruction theory for representing homotopy classes of surfaces in 4-manifolds by immersions with pairwise disjoint images is developed, using the theory of non-repeating Whitney towers. The accompanying higher-order intersection…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…