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Tangles, relative
character varieties, and holonomy perturbed traceless flat
moduli spaces
Guillem Cazassus, Chris Herald and Paul Kirk |
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Vol. 5 (2022), No. 1, 95–121
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Abstract |
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We prove that the restriction map from the subspace of regular points of the holonomy perturbed SU(2) traceless flat moduli space of a tangle in a 3-manifold to the traceless flat moduli space of its boundary marked surface is a Lagrangian immersion. A key ingredient in our proof is the use of composition in the Weinstein category, combined with the fact that SU(2) holonomy perturbations in a cylinder induce Hamiltonian isotopies. In addition, we show that , the 2-sphere with four marked points, is its own traceless flat SU(2) moduli space. |
Keywords
holonomy perturbation, Lagrangian immersion, Floer
homology, flat moduli space, traceless character variety,
quilted Floer homology
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Mathematical Subject Classification
Primary: 57K18, 57K31, 57R58
Secondary: 81T13
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Milestones
Received: 31 January 2021
Revised: 23 April 2021
Accepted: 3 May 2021
Published: 27 October 2022
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Authors |
| Guillem Cazassus | |
| Mathematical Institute, University
of Oxford Oxford United Kingdom |
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| Chris Herald | |
| Department of Mathematics and
Statistics University of Nevada Reno, NV United States |
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| Paul Kirk | |
| Department of Mathematics Indiana University Bloomington, IN United States |
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