The Gordon-Litherland pairing for knots in thickened surfaces
报告题目(Title)：The Gordon-Litherland pairing for knots in thickened surfaces
报告人(Speaker)：Hans Boden (McMaster University)
地点(Place)：ZOOM 会议 ID: 686 995 93236 密码：123456
时间(Time)：2021年2月19日 10:00-11:00
邀请人(Inviter)：程志云
报告摘要
We introduce the Gordon-Litherland pairing for knots and links in thickened surfaces that bound unoriented spanning surfaces. Using the GL pairing, we define signature and determinant invariants. We relate the invariants to those derived from the Tait graph and Goeritz matrices. These invariants depend only on the $S^*$ equivalence class of the spanning surface, and the determinants give a simple criterion to check if the knot or link is minimal genus. The GL pairing is isometric to the relative intersection pairing on a 4-manifold obtained as the 2-fold cover along the surface. These results are joint work with M. Chrisman and H. Karimi. One can also use the GL pairing to give a topological characterization of alternating links in thickened surfaces, extending the results of J. Greene and J. Howie.
