Summary: Applications of Homological Algebra Introduction to Perverse Sheaves
Spring 2007 P. Achar
Office: 266 Lockett Hall
Office hours: Tues. 2:00pm3:30pm or by appointment
Introduction. Sheaves on topological spaces are an important tool in many different areas of mathematics.
"Perverse sheaves" are the objects of a category that is closely related to the category of sheaves. Constructing
this category is rather difficult, but the payoff is enormous: in many ways, perverse sheaves have better
properties and are easier to work with than ordinary sheaves, and a number of important advances in
mathematics in the past 25 years could not have taken place without them.
Outline. Most of the semester will be spent developing the background needed to define and establish the
basic properties of perverse sheaves. In the last few weeks of the semester, we will look at a few of their
applications. A tentative schedule for the semester is as follows (each numbered entry stands for one week):
A. Sheaves 8. Rf, f-1
, RHom, L
, RHom, R
1. Definition and basic properties 9. f!
; adjointness properties