Degree
Doctor of Philosophy (PhD)
Department
Department of Mathematics
Document Type
Dissertation
Abstract
Given a Legendrian knot in (R^3, ker(dz − ydx)) one can assign a combinatorial invariants called ruling polynomials. These invariants have been shown to recover not only a (normalized) count of augmentations but are also closely related to a categorical count of augmentations in the form of the homotopy cardinality of the augmentation category. In this article, we prove that that the homotopy cardinality of the n-dimensional represen- tation category is a multiple of the n-colored ruling polynomial. Along the way, we establish that two n-dimensional representations are equivalent in the representation category if they are “conjugate homotopic”. We also provide some applications to Lagrangian concordance.
Date
3-21-2024
Recommended Citation
Murray, Justin, "The Homotopy Cardinality of the Representation Category" (2024). LSU Doctoral Dissertations. 6372.
https://repository.lsu.edu/gradschool_dissertations/6372
Committee Chair
Shea Vela-Vick