Sutured manifolds and polynomial invariants from higher rank bundles

Daemi, Aliakbar¹ ; Xie, Yi²

¹ Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY, United States
² Beijing International Center for Mathematical Research, Peking University, Beijing, China

Geometry & topology, Tome 24 (2020) no. 1, pp. 49-178.

Résumé

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 $N$. 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.

Détail

DOI : 10.2140/gt.2020.24.49

Classification : 57M27, 57R57, 57R58
Keywords: sutured manifolds, higher rank Donaldson invariants, instanton Floer homology, Smith conjecture

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