An introduction to surgery

The goal of this survey talk is to provide an introduction to surgery theory.  Generally speaking, surgery theory is concerned with the classification of high-dimensional manifolds, where high means greater or equal to 4.  Surgery allows us to study the existence and uniqueness of manifold structures within a prescribed homotopy type, dealing with the following questions:

 

1) "Can we find a manifold within a homotopy type?"  

2) "When is a homotopy equivalence of m-dimensional manifolds homotopic to a homeomorphism?"

 

The structure set plays an important role in answering these questions.  In the talk, I will provide definitions and give examples of manifolds with non-trivial structure sets.    Furthermore, the structure set fits into the surgery exact sequence, which is a main result of surgery and an important computational tool. 

 

This is the first of three talks in the following series. 

 

Series title: Applied surgery

Series abstract: Surgery is the key tool for classifying manifolds, up to homeomorphism or diffeomorphism.    This sequence of talks will give an introduction to this tool, and then apply it to specific questions in four manifold topology.

Meeting ID: 916 5855 1117
Password: as before.
Contact: Aru Ray and Tobias Barthel.