The purpose of this paper and its sequel is to determine the homotopy groups of the spectrum THH(`). Here p is an odd prime, ` is the Adams summand of p-local connective K-theory (see for example [25]) and THH is the topological Hochschild homology construction introduced by Bökstedt in [3]. In the present paper we will determine the mod p homotopy groups of THH(`) and also the integral homotop...

Humans have an excellent ability to select a particular sound source from a noisy environment, called the \Cocktail-Party E ect" and to compensate for physically missing sound, called the \Illusion of Continuity." This paper proposes a spectral peak tracker as a model of the illusion of continuity (or phonemic restoration) and a spectral sequence prediction method using a spectral peak tracker....

In [5] we constructed an abelian category A(G) of sheaves over a category of closed subgroups of the r-torus G and showed it can be used as the basis of a finite Adams spectral sequence for calculating groups of stable G-maps. In the present paper we make an algebraic study of the category A(G). We show how to separate information from isotropy groups with the same identity component, giving an...

Working in the context of symmetric spectra, we consider any higher algebraic structures that can be described as algebras over an operad O. We prove that the fundamental adjunction comparing O-algebra spectra with coalgebra spectra over the associated comonad K, via topological Quillen homology (or TQ-homology), can be turned into an equivalence of homotopy theories by replacing O-algebras wit...