Seifert-Torres formulas for the Alexander polynomial of links from quantum sl2

YMSC Topology Seminar

Organizers：

陈伟彦、高鸿灏、黄意、林剑锋、孙巍峰

Speaker：

Matthew HARPER

Michigan State

Time：

Thur., 15:45-16:45, Dec. 19, 2024

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 405 416 0815

Passcode: 111111

Title：

Seifert-Torres formulas for the Alexander polynomial of links from quantum sl2

Abstract:

I will recall how the Alexander polynomial, a classical knot invariant, can be constructed as a quantum invariant from representations of quantum sl2 at a fourth root of unity. Further investigation of the representation theory leads to a diagrammatic calculus which allows us to simplify computations. As an application, we compute the Alexander polynomial for certain types of satellite links using quantum algebraic methods, rather than methods of classical topology.