An introduction to 4-manifolds

Geometry Topology Student Seminar
Wednesday, August 30, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Sierra Knavel – Georgia Tech –
Sierra Knavel

In the early 80's, Freedman discovered that the Whitney trick could be performed in 4-dimensions which quickly led to a complete classification of closed, simply connected topological 4-manifolds. With gauge theory, Donaldson showed that 4-manifolds differ greatly from their higher dimensional counterparts which uncovered the stark differences between topological and smooth results in dimension 4. In this introductory talk, we will give a brief overview this classification and why dimension 4 is so unique. Then, we will describe handlebody decompositions of 4-manifolds and draw several Kirby pictures representing some basic 4-mfds.