SMS scnews item created by Catherine Meister at Thu 16 Apr 2026 1020
Type: Seminar
Distribution: World
Expiry: 11 Jun 2026
Calendar1: 27 May 2026 1200-1300
CalLoc1: SMRI Seminar Room (A12 Macleay Room 301)
CalTitle1: Symmetry groups of hyperbolic flat fully augmented links and their complements
Auth: cmeister@ac02gr132pn7c.shared.sydney.edu.au (cmei0631) in SMS-SAML

Geometry & Topology Seminar: Millichap

Symmetry groups of hyperbolic flat fully augmented links and their complements

Christian Millichap, Furman University

Geometry & Topology Seminar, Wednesday 27th May 2026, 12 pm – 1 pm, SMRI Seminar Room (A12 Macleay Room 301)

Abstract:In this talk, we will first introduce flat fully augmented links, a class of hyperbolic links whose complements admit particularly tractable geometric structures. We will then discuss how a 3-connected, planar, cubic graph called a crushtacean encodes many, and sometimes all, of the orientation-preserving symmetries of a flat fully augmented link and its complement in

S^{3}

. This combinatorial dictionary helps us show that the orientation-preserving symmetry groups of (b-prime) flat fully augmented links correspond exactly with the finite subgroups of

O (3)

. Furthermore, given any finite subgroup

G

O (3)

, our work provides a simple combinatorial construction to explicitly build an infinite class of distinct flat fully augmented links,

L_{i}

, where

S y m^{+} (S^{3}, L_{i}) ≅ S y m^{+} (S^{3} ∖ L_{i}) ≅ G

. This is joint work with Rollie Trapp (CSUSB).

The Geometry & Topology Seminar will be held on the second and fourth Wednesday of the month during semester. The Australian Geometric Topology Webinar will be broadcast at the same time and place on the first and third Wednesday of the month. For seminar updates, see Geometry & Topology Seminar.

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