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Applications of Homological Algebra Introduction to Perverse Sheaves Spring 2007 P. Achar
 

Summary: Applications of Homological Algebra Introduction to Perverse Sheaves
Spring 2007 P. Achar
Proper Pull-Back and PoincarŽe­Verdier Duality
March 13, 2007
Convention. We now add an assumption to our standing list of assumptions on topological spaces. For
each topological space X, we assume there is a number r such that for any exact sequence
F0
· · · Fr
0
of sheaves on X, if F0
, . . . , Fr-1
are all soft, then so is Fr
. (This assumption is true for manifolds and for
closed subsets of manifolds.)
We also add a hypothesis on sheaves. From now on, all sheaves will be assumed to be sheaves of finite-
dimensional vector spaces, and ShX will denote the category of such sheaves.
The main result in this set of notes is the following.
Theorem 1. Let f : X Y be a continuous map. There is a functor f!
: D+
(ShY ) D+

  

Source: Achar, Pramod - Department of Mathematics, Louisiana State University

 

Collections: Mathematics