Unstable multiplicative cohomology operations

Stable and Unstable Operations in mod p Cohomology Theories

We consider operations between two multiplicative, complex orientable cohomology theories. Under suitable hypotheses, we construct a map from unstable to stable operations, left-inverse to the usual map from stable to unstable operations. In the main example, where the target theory is one of the Morava K-theories, this provides a simple and explicit description of a splitting arising from the ...

Multiplicative structure in equivariant cohomology

We introduce the notion of a strongly homotopy-comultiplicative resolution of a module coalgebra over a chain Hopf algebra, which we apply to proving a comultiplicative enrichment of a well-known theorem of Moore concerning the homology of quotient spaces of group actions. The importance of our enriched version of Moore’s theorem lies in its application to the construction of useful cochain alg...

Multiplicative Operations in Bp*bp

where S is the Landweber-Novikov algebra. S has the added advantage of being a cocommutative Hopf algebra over Z. This paper does not remove this difficulty, but we will show that the monoid of multiplicative operations in BP*BP, (i.e. those operations which induce ring endomorphisms on BP*X for any space X)9 which we will denote by Γ{BP), has a submonoid analogous to the monoid of multiplicati...

Cohomology operations and algebraic geometry

This manuscript is based on a ten hours series of seminars I delivered in August of 2003 at the Nagoya Institute of Technology as part of the workshop on homotopy theory organized by Norihiko Minami and following the Kinosaki conference in honor of Goro Nishida. One of the most striking applications of homotopy theory in “exotic” contexes is Voevodsky’s proof of the Milnor Conjecture. This conj...

Stable Operations in Generalized Cohomology