Results 1  10
of
122
Absolutely graded Floer homologies and intersection forms for fourmanifolds with boundary
 Advances in Mathematics 173
, 2003
"... Abstract. In [22], we introduced absolute gradings on the threemanifold invariants developed in [21] and [20]. Coupled with the surgery long exact sequences, we obtain a number of three and fourdimensional applications of this absolute grading including strengthenings of the “complexity bounds ” ..."
Abstract

Cited by 101 (26 self)
 Add to MetaCart
Abstract. In [22], we introduced absolute gradings on the threemanifold invariants developed in [21] and [20]. Coupled with the surgery long exact sequences, we obtain a number of three and fourdimensional applications of this absolute grading including strengthenings of the “complexity bounds ” derived in [20], restrictions on knots whose surgeries give rise to lens spaces, and calculations of HF + for a variety of threemanifolds. Moreover, we show how the structure of HF + constrains the exoticness of definite intersection forms for smooth fourmanifolds which bound a given threemanifold. In addition to these new applications, the techniques also provide alternate proofs of Donaldson’s diagonalizability theorem and the Thom conjecture for CP 2. 1.
Lectures on 2D YangMills Theory, Equivariant Cohomology and Topological Field Theories
, 1996
"... These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying ..."
Abstract

Cited by 97 (7 self)
 Add to MetaCart
These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.
Gauge theory for embedded surfaces
 I, Topology
, 1993
"... (i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly ..."
Abstract

Cited by 68 (6 self)
 Add to MetaCart
(i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly
A stable cohomotopy refinement of SeibergWitten invariants: I, Preprint, available at www.mathematik.unibielefeld.de/˜bauer
"... Abstract. A gluing theorem for the stable cohomotopy invariant defined in the first article in this series of two gives new results on diffeomorphism types of decomposable manifolds. 1. ..."
Abstract

Cited by 50 (3 self)
 Add to MetaCart
Abstract. A gluing theorem for the stable cohomotopy invariant defined in the first article in this series of two gives new results on diffeomorphism types of decomposable manifolds. 1.
StateSum Invariants of 4Manifolds
 J. Knot Theory Ram
, 1997
"... Abstract: We provide, with proofs, a complete description of the authors ’ construction of statesum invariants announced in [CY], and its generalization to an arbitrary (artinian) semisimple tortile category. We also discuss the relationship of these invariants to generalizations of Broda’s surgery ..."
Abstract

Cited by 30 (6 self)
 Add to MetaCart
Abstract: We provide, with proofs, a complete description of the authors ’ construction of statesum invariants announced in [CY], and its generalization to an arbitrary (artinian) semisimple tortile category. We also discuss the relationship of these invariants to generalizations of Broda’s surgery invariants [Br1,Br2] using techniques developed in the case of the semisimple subquotient of Rep(Uq(sl2)) (q a principal 4r th root of unity) by Roberts [Ro1]. We briefly discuss the generalizations to invariants of 4manifolds equipped with 2dimensional (co)homology classes introduced by Yetter [Y6] and Roberts [Ro2], which are the subject of the sequel. 1 1
PU(2) monopoles, I: Regularity, Uhlenbeck compactness, and transversality
 J. DIFFERENTIAL GEOM
, 1997
"... ..."
Curvature, connected sums, and SeibergWitten theory
 Comm. Anal. Geom
"... We consider several differentialtopological invariants of compact 4manifolds which directly arise from Riemannian variational problems. Using recent results of Bauer and Furuta [5, 4], we compute these invariants in many cases that were previously intractable. In particular, we are now able to cal ..."
Abstract

Cited by 13 (4 self)
 Add to MetaCart
We consider several differentialtopological invariants of compact 4manifolds which directly arise from Riemannian variational problems. Using recent results of Bauer and Furuta [5, 4], we compute these invariants in many cases that were previously intractable. In particular, we are now able to calculate the Yamabe invariant for many connected sums of complex surfaces. 1
Equivariant aspects of YangMills Floer theory
 Topology
"... This paper is concerned with Floer cohomology groups of SO(3) bundles P → Y, where Y is a closed, oriented 3manifold. Following [4] we only ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
This paper is concerned with Floer cohomology groups of SO(3) bundles P → Y, where Y is a closed, oriented 3manifold. Following [4] we only