$SO(3)$-Floer homology of 3-manifolds with boundary 1

Abstract

In this paper the author discuss the relation between Lagrangian Floer homology and Gauge-theory (Donaldson theory) Floer homology. It can be regarded as a version of Atiyah-Floer type conjecture in the case of $SO(3)$-bundle with non-trivial second Stiefel-Whitney class. This is a first of a series of papers, where we describe the main results and geometric and algebraic parts of the proof. The half of analytic detail was in [Fu5] which was published in 1998. The other half will appear in subsequent papers.

arXiv comment80 pages 41 figures

References in corpus (7)

• Technical details on Kuranishi structure and virtual fundamental chain
• Kuranishi structure, Pseudo-holomorphic curve, and Virtual fundamental chain: Part 1
• A tour of bordered Floer theory
• Floer field theory for tangles
• Gromov-Uhlenbeck Compactness
• The Künneth theorem for the Fukaya algebra of a product of Lagrangians
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Cited by in corpus (3)

• Functors of wrapped Fukaya categories from Lagrangian correspondences
• Wrapped Floer cohomology and Lagrangian correspondences
• Lagrangian correspondences and the generalized Viterbo restriction functor