The correspondence induced on the pillowcase by the earring tangle
Geometric Topology
2022-10-26 v2 Symplectic Geometry
Abstract
The earring tangle consists of four strands 4pt x [0,1] inside S^2 x [0,1] and one meridian around one of the strands. Equipping this tangle with a nontrivial SO(3) bundle, we show that its traceless SU(2) flat moduli space is topologically a smooth genus three surface. We also show that the restriction map from this surface to the traceless flat moduli space of the boundary of the earring tangle is a particular Lagrangian immersion into the product of two pillowcases. The latter computation suggests that figure eight bubbling -- a subtle degeneration phenomenon predicted by Bottman and Wehrheim -- appears in the context of traceless character varieties.
Keywords
Cite
@article{arxiv.2010.04320,
title = {The correspondence induced on the pillowcase by the earring tangle},
author = {Guillem Cazassus and Christopher M. Herald and Paul Kirk and Artem Kotelskiy},
journal= {arXiv preprint arXiv:2010.04320},
year = {2022}
}
Comments
To appear in Journal of Topology