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Michael Ching
Steenrod Operations, Group Homology and Simplicial Cocommutative Coalgebras
Abstract:
The cohomology groups of a topological space X with coefficients in F_p
support funny operations called 'Steenrod squares' (if p = 2) or 'reduced
powers operations' in general. Why? The short answer is because the
diagonal map
d : X -> X x X
is cocommutative up to homotopy. That is, if T is the map from X x X to
itself that switches the factors then Td is homotopic to d. The long
answer will hopefully take about 50 minutes to describe.
(The more observant among you will notice that in fact Td = d so that d is
strictly cocommutative. If time and speaker's preparation permit we will
see what the consequences of this are.)
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