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2:30 pm Thursday, October 1, 2009 Current Math Seminar: An Introduction to Cellular Homology, Covering Spacesby James Cooper, Derek Goto (Rice University) in HB 227- James Cooper: Homology is a tool that we use to find the higher dimensional holes that the fundamental group fails to find. This provides us another topological invariant we may use to distinguish between spaces. I define a cellular complex and n-chains on that complex. With a boundary operator, we form a chain of abelian groups of these chains. We then use this sequence of groups to define homology. I will end with examples of computing homology and, time permitting, the statement of the Mayer–Vietoris sequence. Derek Goto: The correspondence between covering spaces and deck groups is basically Galois theory in another category. I will talk about this and go over some relevant examples. If there is time, I will say a bit about Cayley complexes.
Submitted by sm29@rice.edu |