Sutures, quantum groups and topological quantum field theory
by Daniel Mathews
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.