Sutured Manifolds and Polynomial Invariants from Higher Rank Bundles

Aliakbar Daemi; Yi Xie

doi:10.2140/gt.2020.24.49

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arXiv · 1701.00571

Sutured Manifolds and Polynomial Invariants from Higher Rank Bundles

Aliakbar Daemi·Yi Xie

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Abstract

For each integer $N\geq 2$, 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.

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BibTeX RIS

Aliakbar Daemi, Yi Xie. 2018-03-25. Sutured Manifolds and Polynomial Invariants from Higher Rank Bundles. https://doi.org/10.2140/gt.2020.24.49

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