Algebro-geometric cohomology theories are described axiomatically, with a systematic treatment of their orientations. For every oriented theory, transfer mappings are constructed for mappings of smooth varieties that are proper on supports. In some basic cases, transfers are calculated. The presentation is illustrated by motivic cohomology, K-theory, algebraic cobordism, and other examples. The...

Building up on work of Epstein, May and Drury, we define investigate the mod $p$ Steenrod operations de Rham cohomology smooth algebraic stacks over a field characteristic $p>0$. We then compute action classifying for finite groups, connected reductive groups which is not torsion prime, (special) orthogonal when $p=2$.

Introduction. In our earlier papers [2,3,4,5,6], we investigated stable operations and cooperations in elliptic cohomology and its variants, relating these to known operations on rings of modular forms. The purpose of this article is to give an introduction to these stable operation algebras, in particular explaining the connections with Hecke algebras and Morava stabilizer algebras; further de...

The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.

We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The selfdistributive operations of these structures provide solutions of the Yang–Baxter equation, and, conversely, solutions of the Ya...

There is much we still do not know about projective spaces. We describe here how the mod two cohomology of each real projective space is built as an unstable module over the Steenrod algebra A, or equivalently, over K, the algebra of inherently unstable mod two “lower operations” originally introduced by Steenrod. In particular, to produce the cohomology of projective space of each dimension we...

Let T (j) be the dual of the jth stable summand of Ω2S3 (at the prime 2) with top class in dimension j. Then it is known that T (j) is a retract of a suspension spectrum, and that the homotopy colimit of a certain sequence T (j) → T (2j) → . . . is an infinite wedge of stable summands of K(V, 1)’s, where V denotes an elementary abelian 2 group. In particular, when one starts with T (1), one get...