Holomorphic triangles and invariants for smooth four-manifolds

Abstract

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 endows the corresponding three-dimensional theories with additional structure: an absolute grading of certain of its Floer homology groups. The cornerstone of these constructions is the study of holomorphic disks in the symmetric products of Riemann surfaces.

73 pages, 6 figures

References in corpus (1)

• Holomorphic disks and three-manifold invariants: properties and applications

Cited by in corpus (16)

• Floer homology and knot complements
• Holomorphic disks and three-manifold invariants: properties and applications
• Heegaard Floer homologies and contact structures
• Tight contact structures and genus one fibered knots
• Planar open books and Floer homology
• Holomorphic disks and topological invariants for closed three-manifolds
• Knot Floer homology, genus bounds, and mutation
• On Floer homology and the Berge conjecture on knots admitting lens space surgeries
• Holomorphic disks and knot invariants
• The Dehn surgery characterization of the trefoil and the figure eight knot
• Maslov index formulas for Whitney n-gons
• On the Slicing Genus of Legendrian Knots
• On the Heegaard Floer homology of branched double-covers
• Knots with unknotting number one and Heegaard Floer homology
• Holomorphic triangle invariants and the topology of symplectic four-manifolds
• On rational blow-downs in Heegaard-Floer homology