#### Volume 24, issue 1 (2020)

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Sutured manifolds and polynomial invariants from higher rank bundles

### Aliakbar Daemi and Yi Xie

Geometry & Topology 24 (2020) 49–178
##### 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 $N\phantom{\rule{-0.17em}{0ex}}$. We confirm the predictions of Mariño and Moore 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 is exploited to define a Floer homology theory for sutured $3$–manifolds.

##### Keywords
sutured manifolds, higher rank Donaldson invariants, instanton Floer homology, Smith conjecture
##### Mathematical Subject Classification 2010
Primary: 57M27, 57R57, 57R58
##### Publication
Revised: 25 March 2019
Accepted: 20 May 2019
Published: 25 March 2020
Proposed: Simon Donaldson
Seconded: Ciprian Manolescu, Peter Ozsváth
##### Authors
 Aliakbar Daemi Simons Center for Geometry and Physics State University of New York Stony Brook, NY United States Yi Xie Beijing International Center for Mathematical Research Peking University Beijing China