Topology Seminar

Date: November 4, 2020

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Sanjay Kumar, Michigan State University

Title: Fundamental shadow links realized as links in the 3-sphere

Abstract: In this talk, I will discuss two conjectures which relate quantum topology and hyperbolic geometry. Chen and Yang conjectured that the asymptotics of the Turaev-Viro invariants determine the hyperbolic volume of the 3-manifold, and Andersen, Masbaum, and Ueno (AMU) conjectured for a surface that the asymptotics of the quantum representations reflect certain geometric properties of the mapping class group. For a manifold M(f) constructed as the mapping tori of an element f in the mapping class group, Detcherry and Kalfagianni showed that M(f) satisfying the Turaev-Viro invariant volume conjecture implies that f satisfies the AMU conjecture. Using techniques from Turaev's shadow theory, I construct infinite families of links in the 3-sphere with complement homeomorphic to the complement of fundamental shadow links which are a class of links in connected sums of S^2 times S^1 that satisfy the Turaev-Viro invariant volume conjecture. Through homeomorphisms, these link complements in S^3 can be realized as the mapping tori for explicit elements in the mapping class group providing families that satisfy the AMU conjecture. Video recording is available at https://tamu.zoom.us/rec/share/NVDt4tmOzD6DyGdOfO8XTjBCMBG0d_BK4grFJPN35hrSa7b-N_0rD1MS_OfLEOWK.OV72bu9Mc4g3cwyL (Access Password: 13TuT+XF)