# Sutures, quantum groups and topological quantum field theory

Algebra/Geometry/Topology Seminar

#### by Daniel Mathews

Institution: Monash University
Date: Fri 24th May 2013
Time: 3:15 PM
Location: 213 Richard Berry

Abstract: Much recent work in topology is based on the ideas of categorification, quantum groups and topological quantum field theory (TQFT). We demonstrate a particularly simple case, which is work in progress, illustrating all of these ideas. Using nothing more than curves on surfaces --- sutures, to be precise --- we build a TQFT, related to Heegaard Floer homology, and demonstrate, following recent work of Tian, quantum sl(1|1) actions via a quantized version of the Temperley--Lieb algebra. This in turn is based on creation and annihilation operators'' which can be seen as processing qubits, topology or quantum group representations. No knowledge of quantum groups, Heegaard Floer homology or categorification will be assumed.