Mark Hovey (Wesleyan University and the Newton Institute)
mhovey@wesleyan.edu
For many homology theories E(X) defined on topological spaces X, E(X) is more than an abelian group or even a module over E(point); it is also a comodule over the Hopf algebroid E(E). We show that for many of the common homology theories E, the category of comodules over E(E) depends up to equivalence only on the heights of E at the different primes. In particular, we give several important examples of homology theories E and F such that the categories of comodules over E(E) and F(F) are equivalent, even though the categories of modules over E(point) and F(point) are very different. Thus these theories contain the same information about X in a very strong sense.
This is joint work with Neil Strickland of the University of Sheffield.