On stable functional cohomology operations

Stable Operations in Generalized Cohomology

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 ...

On the Steenrod Operations in Cyclic Cohomology

For a commutative Hopf algebra A over Z/p, where p is a prime integer, we define the Steenrod operations P i in cyclic cohomology of A using a tensor product of a free resolution of the symmetric group S n and the standard resolution of the algebra A over the cyclic category according to Loday (1992). We also compute some of these operations. 1. Introduction. For any prime p, the mod p Steenrod...

Notes on Stable Maps and Quantum Cohomology

0.1. Overview. The aim of these notes is to describe an exciting chapter in the recent development of quantum cohomology. Guided by ideas from physics (see [W]), a remarkable structure on the solutions of certain rational enumerative geometry problems has been found: the solutions are coefficients in the multiplication table of a quantum cohomology ring. Associativity of the ring yields non-tri...

On the Cohomology of Stable Map Spaces

We describe an approach to calculating the cohomology rings of stable map spaces M0,0(P n, d).