X iv : d g - ga / 9 70 20 04 v 1 7 F eb 1 99 7 DONALDSON INVARIANTS FOR CONNECTED SUMS ALONG SURFACES OF GENUS 2

ar X iv : d g - ga / 9 50 70 04 v 1 2 4 Ju l 1 99 5 LOCALISATION OF THE DONALDSON ’ S INVARIANTS ALONG SEIBERG - WITTEN CLASSES

This article is a first step in establishing a link between the Donaldson polynomials and Seiberg-Witten invariants of a smooth 4-manifold.

ar X iv : q - a lg / 9 70 20 09 v 1 6 F eb 1 99 7 The Fundamental Theorem of Vassiliev Invariants

1 Topology (and Combinatorics) 3 1.1 Vassiliev invariants and the Fundamental Theorem . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Hutchings’ combinatorial-topological approach . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Hutchings’ condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 A possible strategy. . . . . . . . . . . . . . . ...

Seiberg-witten-floer Homology of a Surface times a Circle

We determine the Seiberg–Witten–Floer homology groups of the 3-manifold Σ × S 1, where Σ is a surface of genus g � 2, together with its ring structure, for a Spin� structure with non-vanishing first Chern class. We give applications to computing Seiberg–Witten invariants of 4-manifolds which are connected sums along surfaces and also we reprove the higher type adjunction inequalities obtained b...

ar X iv : d g - ga / 9 71 20 20 v 1 3 0 D ec 1 99 7 Weinstein Conjecture and GW Invariants

Gluing Formulae for Donaldson Invariants for Connected Sums along Surfaces

Following our work in [18], we prove a gluing formula for the Donaldson invariants of the connected sum of two four-manifolds along surfaces of the same genus g, self-intersection zero and representing odd homology classes, solving a conjecture of Morgan and Szabó [14].