Related papers: Equivariant instanton homology

Using Furuta's idea of finite dimensional approximation in Seiberg-Witten theory, we refine Seiberg-Witten Floer homology to obtain an invariant of homology 3-spheres which lives in the S^1-equivariant graded suspension category. In…

In \cite{MR1957829}, Ozsv\'ath and Szab\'o use Heegaard Floer homology to define numerical invariants $d_{1/2}$ and $d_{-1/2}$ for 3-manifolds $Y$ with $H_{1}(Y;\mathbb{Z})\cong \mathbb{Z}$. We define involutive Heegaard Floer theoretic…

The aim of this article is to introduce invariants of oriented, smooth, closed four-manifolds, built using the Floer homology theories defined in two earlier papers (math.SG/0101206 and math.SG/0105202). This four-dimensional theory also…

Building on ideas from [DT98; DS11; Wal17; Hay17], we outline a proposal for constructing Floer homology groups associated with a G2-manifold. These groups are generated by associative submanifolds and solutions of the ADHM Seiberg-Witten…

We make use of the action of $H_1(Y)$ in Heegaard Floer homology to generalize the Ozsv\'ath-Szab\'o correction terms for $3$-manifolds with standard $\operatorname{HF}^\infty$. We establish the basic properties of these invariants:…

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…

Bordered Heegaard Floer homology is a three-manifold invariant which associates to a surface F an algebra A(F) and to a three-manifold Y with boundary identified with F a module over A(F). In this paper, we establish naturality properties…

Inspired by the Ozsv\'ath-Szab\'o mixed invariant in ordinary Heegaard Floer theory, we define a mixed invariant $\Phi_{X, \mathfrak{s}}^{I}$ for closed, spin four-manifolds $(X, \mathfrak{s})$ using the cobordism maps on involutive…

Bordered Floer homology is an invariant for 3-manifolds with boundary, defined by the authors in 2008. It extends the Heegaard Floer homology of closed 3-manifolds, defined in earlier work of Zolt\'an Szab\'o and the second author. In…

Motivated by a conjecture of Donaldson and Segal, we take a first step towards defining a new 3-manifold Floer theory, where the complex is defined by a count of Fueter sections of a hyperk\"ahler bundle over the 3-manifold with fibers…

The singular instanton Floer homology was defined by Kronheimer and Mrowka in connection with their proof that the Khovanov homology is an unknot detector. We study this theory for knots and two-component links using equivariant gauge…

For any link of two components in an integral homology sphere, we define an instanton Floer homology whose Euler characteristic is the linking number between the components of the link. We relate this Floer homology to the Kronheimer-Mrowka…

Building on the algebraic framework developed by Hendricks, Manolescu, and Zemke, we introduce and study a set of Floer-theoretic invariants aimed at detecting corks. Our invariants obstruct the extension of a given involution over any…

We consider a stabilized version of hat Heegaard Floer homology of a 3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial algorithm for constructing this invariant, starting from a…

(In the revised version the relevant aspect of noncompactness of the moduli of instantons is discussed. It is shown nonperturbatively that any BRST trivial deformation of A-model which does not change the ranks of BRST cohomology does not…

We continue our study of the integer-valued knot invariants $\nu^\sharp(K)$ and $r_0(K)$, which together determine the dimensions of the framed instanton homologies of all nonzero Dehn surgeries on $K$. We first establish a "conjugation"…

We define a "real" version of Kronheimer-Mrowka's monopole Floer homology for a 3-manifold equipped with an involution. As a special case, we obtain invariants for links via their double branched covers. The new input is the notion of a…

Suppose H is an admissible Heegaard diagram for a balanced sutured manifold (M,\gamma). We prove that the number of generators of the associated sutured Heegaard Floer complex is an upper bound on the dimension of the sutured instanton…

Seiberg-Witten (Floer) theory, Ozsvath-Szabo's Heegaard Floer theory, Hutchings's embedded contact homology, in different stages of development, define (or are expected to define) packages of invariants for 3- and 4-manifolds (including…

We prove first-order naturality of involutive Heegaard Floer homology, and furthermore construct well-defined maps on involutive Heegaard Floer homology associated to cobordisms between three-manifolds. We also prove analogous naturality…