1. Even periodic ring theories and formal group laws 1 2. Formal groups 5 3. Geometry of formal groups 8 4. Heights of formal groups 12 5. Homology of Z× BU and related spaces 15 6. The Thom isomorphism 19 7. Elliptic spectra 24 8. The generalized Weierstrass equation 25 9. Modular forms 29 10. Elliptic curves and the group structure 30 11. Weierstrass parameters and Thom spectrum of ΩU(4) 33 1...

An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a non-commutative C-algebra associated to a bundle E → M , equipped with a compatible connection ∇, which plays the role of the algebra of functions on the infinit...

We identify the topological Hochschild homology (THH) of the Thom spectrum associated to an E∞ classifying map X → BG, for G an appropriate group or monoid (e.g. U , O, and F ). We deduce the comparison from the observation of McClure, Schwanzl, and Vogt that THH of a cofibrant commutative S-algebra (E∞ ring spectrum) R can be described as an indexed colimit together with a verification that th...

Ando, Matsuzawa, Thom, and Törnquist have resolved a problem by Sorin Popa constructing an example of Polish group unitary operators with the strong operator topology, whose left right uniform structures coincide, but which does not embed into