Year: 2025
Type: article
Abstract: We prove a conjecture of Lê and Sikora by providing a comparison between various existing $SL_n$ skein theories. While doing so, we show that the full subcategory of the spider category, $\mathcal {S}p(SL_n)$ , defined by Cautis–Kamnitzer–Morrison, whose objects are monoidally generated by the standard representation and its dual, is equivalent as a spherical braided category to Sikora’s quotient category. This also answers a question from Morrison’s Ph.D. thesis. Finally, we show that the skein modules associated with the CKM and Sikora’s webs are isomorphic.
Source: Canadian Journal of Mathematics
Author: Anup Poudel
Institution: The Ohio State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4409208584