Sutured Manifolds and Polynomial Invariants from Higher Rank Bundles

Abstract

For each integer $N\ge 2$, Mariño and Moore defined generalized Donaldson invariants by the methods of quantum field theory, and made predictions about the values of these invariants. Subsequently, Kronheimer gave a rigorous definition of generalized Donaldson invariants using the moduli spaces of anti-self-dual connections on hermitian vector bundles of rank $N$. In this paper, Mariño and Moore's predictions are confirmed for simply connected elliptic surfaces without multiple fibers and certain surfaces of general type in the case that $N=3$. The primary motivation is to study 3-manifold instanton Floer homologies which are defined by higher rank bundles. In particular, the computation of the generalized Donaldson invariants are exploited to define a Floer homology theory for sutured 3-manifolds.

105 pages, 5 figures. v2: exposition of gluing theory results improved, typos and minor mistakes fixed

References in corpus (2)

• Sutures and contact homology I
• Surgery, Polygons and $SU(N)$-Floer Homology

Cited by in corpus (2)

• Chern-Simons Functional and the Homology Cobordism Group
• Gauge theories on compact toric manifolds