February 1: Tetsuya Nakamura – Spin Structures on a Band

Please join us in LGRT 1528 on Wednesday, 2/1/17 from 5 pm to 6 pm for the first talk of the Spring semester. We’ll hear from our own co-organizer Tetsuya Nakamura about a concept important to geometry, topology, and physics: spin structure. The talk will focus on examples and make use of clever visual aids. There will also be pizza and soda!

Here’s an abstract:

Spin Structure on a band:

Gluing two edges of a strip, we can make a closed band in a ring form. If we twist by a half turn before gluing, we get the famous Mobius band. If we perform a full twist and then glue the edges, we get a “more” twisted band, which as a surface, is still considered to be the same as the “non-twisted” band. In fact, any band with integer twists is considered the same as the non-twisted one, even though they look different in reality. In the talk we introduce the so called spin structure on the band, which recognizes this parity of twisting. In other words, we can distinguish amounts of half-twisting mod 4 by considering the band (surface) with the spin structure on it. We will give different definitions of the spin structure on a band and see how they are related to each other. These are demonstrated using papers, ropes and other materials, so we will use less mathematical formulas.

GSspinstrS1disk

(Image from Gompf and Stipsicz – Four Manifolds and Kirby Calculus)