Four-manifold invariants from higher-rank bundles

TL;DR

This paper extends Donaldson invariants to 4-manifolds using higher-rank gauge groups, computes specific cases, and confirms consistency with theoretical predictions.

Contribution

It introduces generalized invariants for 4-manifolds based on SU(N) and PSU(N) connections, expanding the scope of Donaldson theory.

Findings

Calculated invariants for knot-complement 4-manifolds

Results align with Marino and Moore's predictions

Demonstrated invariants' consistency with existing theories

Abstract

Generalized Donaldson invariants of 4-manifolds are defined, using moduli spaces of anti-self-dual connections with structure group SU(N) or PSU(N). Some values of the invariants are calculated for the case that the 4-manifold arises by the knot-complement construction of Fintushel and Stern. The results are consistent with predictions of Marino and Moore.