Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces

Guillem Cazassus; Chris Herald; Paul Kirk

doi:10.2140/obs.2022.5.95

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arXiv · 2102.00901

Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces

Guillem Cazassus·Chris Herald·Paul Kirk

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Abstract

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 $(S^2,4)$, the 2-sphere with four marked points, is its own traceless flat SU(2) moduli space.

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Guillem Cazassus, Chris Herald, Paul Kirk. 2021-02-01. Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces. https://doi.org/10.2140/obs.2022.5.95

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