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An Introduction to Spectral Sequences
Student-Run Discrete Mathematics| Speaker: | Sonny Mohammadzadeh, UC Davis |
| Location: | 2112 MSB |
| Start time: | Thu, Mar 13 2008, 3:10PM |
Description
Spectral Sequences are an algebraic tool that can be used to calculate the
(co)homology of many algebraic and topological complexes. More
specifically it is an algorithm that involves taking succesive
(co)homology groups of a complex. Standard convergence theorems can be
established to show that a spectral sequence can "approximate" the
(co)homology of the original complex. We will see examples of spectral
sequences, including how to naturally induce a spectral sequence from a
filtration of a complex. Time permitting we will see the Leray-Serre
spectral sequence (invented by Leray as a prisoner of war!) and how it can
be used to calculate the (co)homology of the total space of a fibration
give the (co)homologies of the base and fiber space.