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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 ..."
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Cited by 67 (6 self)
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(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
TOPOLOGICAL MINIMAL GENUS AND L 2SIGNATURES
, 2006
"... Abstract. We obtain new lower bounds of the minimal genus of a locally flat surface representing a 2dimensional homology class in a topological 4manifold with boundary, using the von NeumannCheegerGromov ρinvariant. As an application our results are employed to investigate the slice genus of kn ..."
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Cited by 2 (0 self)
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Abstract. We obtain new lower bounds of the minimal genus of a locally flat surface representing a 2dimensional homology class in a topological 4manifold with boundary, using the von NeumannCheegerGromov ρinvariant. As an application our results are employed to investigate the slice genus of knots. We illustrate examples with arbitrarily large slice genus for which our lower bound is optimal but all previously known invariants vanish. 1. Introduction and
BETWEEN LOWER AND HIGHER DIMENSIONS (in the work of Terry Lawson)
"... There are several approaches to summarizing a mathematician’s research accomplishments, and each has its advantages and disadvantages. This article is based upon a talk given at Tulane that was aimed at a fairly general audience, including faculty members in other areas and graduate students who had ..."
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There are several approaches to summarizing a mathematician’s research accomplishments, and each has its advantages and disadvantages. This article is based upon a talk given at Tulane that was aimed at a fairly general audience, including faculty members in other areas and graduate students who had taken the usual entry level courses. As such, it is meant to be relatively nontechnical and to emphasize qualitative rather than quantitative issues; in keeping with this aim, references will be given for some standard topological notions that are not normally treated in entry level graduate courses. Since this was an hour talk, it was also not feasible to describe every single piece of published mathematical work that Terry Lawson has ever written; in particular, some papers like [42] and [50] would require lengthy digressions that are not easily related to the central themes in his main lines of research. Instead, we shall focus on some ways in which Terry’s work relates to an important thread in geometric topology; namely, the passage from studying problems in a given dimension to studying problems in the next dimensions. Qualitatively speaking, there are fairly welldeveloped theories for very low dimensions and for all sufficiently large dimensions, but between these ranges there are some dimensions in which the answers to many fundamental
Gauge theory for embedded surfaces, II
"... (i) The theorem and an outline of the proof. This paper is the second in a series of two, aimed at developing results about the topology of embedded surfaces Σ in a 4manifold X using some new YangMills moduli spaces associated to such pairs (X,Σ). The moduli spaces were ..."
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(i) The theorem and an outline of the proof. This paper is the second in a series of two, aimed at developing results about the topology of embedded surfaces Σ in a 4manifold X using some new YangMills moduli spaces associated to such pairs (X,Σ). The moduli spaces were
GENERALIZED FIBRE SUMS OF 4MANIFOLDS AND THE CANONICAL CLASS
, 907
"... ABSTRACT. In this article we determine the integral homology and cohomology groups of a closed 4manifold X obtained as the generalized fibre sum of two closed 4manifolds M and N along embedded surfaces of genus g and selfintersection zero. If the homologies of the 4manifolds are torsion free and ..."
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ABSTRACT. In this article we determine the integral homology and cohomology groups of a closed 4manifold X obtained as the generalized fibre sum of two closed 4manifolds M and N along embedded surfaces of genus g and selfintersection zero. If the homologies of the 4manifolds are torsion free and the surfaces represent indivisible homology classes, we derive a formula for the intersection form of X. If the 4manifolds M and N are symplectic and the surfaces symplectically embedded we also derive a formula for the canonical class of the symplectic fibre sum. CONTENTS