In this paper, we use conformal field theory to construct a generalized cohomology theory which has some properties of elliptic cohomology theory which was some properties of elliptic cohomology. A part of our presentation is a rigorous definition of conformal field theory following Segal's axioms, and some examples, such as lattice theories associated with… (More)
With motivation from algebraic topology, algebraic geometry, and string theory, we study various topics in differential homological algebra. The work is divided into five largely independent parts: I Definitions and examples of operads and their actions II Partial algebraic structures and conversion theorems III Derived categories from a topological point… (More)
Using the Landweber}Araki theory of Real cobordism and Real-oriented spectra, we de"ne a Real analogue of the Adams}Novikov spectral sequence. This is a new spectral sequence with a potentially calculable E-term. It has versions converging to either the 9/2-equivariant or the non-equivariant stable 2-stems. We also construct a Real analogue of the… (More)
We describe a formalism allowing a completely mathematical rigorous approach to closed and open conformal field theories with general anomaly. We also propose a way of formalizing modular functors with positive and negative parts, and outline some connections with other topics, in particular elliptic cohomology.
We discuss certain calculations in the 2-complete motivic stable homotopy category over an algebraically closed field of characteristic 0. Specifically , we prove the convergence of motivic analogues of the Adams and Adams-Novikov spectral sequences, and as one application, discuss the 2-complete version of the complex motivic J-homomorphism.
The homotopy limit problem for Karoubi's Hermitian K-theory  was posed by Thomason in 1983 . There is a canonical map from algebraic Hermitian K-theory to the /2-homotopy fixed points of algebraic K-theory. The problem asks, roughly, how close this map is to being an isomorphism, specifically after completion at 2. In this paper, we solve this… (More)
Motivated by complex oriented theories we deene A-equivariant formal group laws for any abelian compact Lie group A, show there is a representing ring for them, and begin the investigation of it. We examine a number of topological cases, including K-theory in some detail. JPCG thanks Hal Sadofsky for many useful conversations, the University of Chicago and… (More)