We meet weekly Thursday 1:00 - 2:00 in MC 5403.
Our main reference is 4-Manifolds and Kirby Calculus by Gompf and Stipsicz, specifically chapters 4 and 5. Here are some additional references which may be helpful:
09/11 Michael Albanese - Blowups and examples!
We will discuss blowups and prove that the blowups of S2 bundles over S2 are diffeomorphic. We will use the remaining time to discuss other examples.
02/11 William Gollinger - Kirby Moves
In this talk we revisit the handle moves introduced earlier, now in the context of Kirby diagrams. We will carefully study the effects of handle slides on framings, and illustrate some handle cancellations. Lastly we'll introduce blow-ups and blow-downs as helpful tools for making Kirby diagrams more amenable.
26/10 Robert Harris - Kirby diagrams cont. - what manifold is this?
We will continue our discussion on Kirby diagrams. In particular we will look at the Kirby diagrams for some well known 4-manifolds and see some of the techniques used for determining what a Kirby diagram for a given manifold should look like.
19/10 Ty Ghaswala - Kirby diagrams - because 3-dimensions just isn't enough
I will introduce Kirby diagrams, which are a way of denoting 4-dimensional handles. The talk will almost entirely consist of staring at pictures of knots and balls and convincing ourselves that these are actually 4-dimensional handlebodies!
28/09 Michael Albanese - Heegaard diagrams of three-manifolds
We will represent handle decompositions of three-manifolds diagramatically, and relate them to Heegaard splittings. This will serve as a precursor for Kirby diagrams.
21/09 William Gollinger - Handles II
This week we continue the discussion of handles, moving on to handle decompositions of smooth manifolds. We briefly describe how Morse Theory ensures the existence of handle decompositions, and give some particular examples. We discuss in some detail the notions of dual decompositions, handle cancellations, and handle slides.
14/09 Michael Albanese - Handles
We introduce handles as the fundamental building blocks of manifolds and begin to discuss the notion of a handle decomposition. The discussion will apply to all dimensions.