Topological cyclic homology is a refinement of Connes–Tsygan's cyclic homology which
was introduced by Bökstedt–Hsiang–Madsen in 1993 as an approximation to algebraic K …

We show that the Kervaire invariant one elements θ_jϵπ_2^j+1-2S^0 exist only for j≤ 6. By
Browder's Theorem, this means that smooth framed manifolds of Kervaire invariant one exist …

Working in the category of based spaces, we give the basic theory of diagram spaces and
diagram spectra. These are functors for a suitable small topological category. When is …

A stable model category is a setting for homotopy theory where the suspension functor is
invertible. The prototypical examples are the category of spectra in the sense of stable …

This book develops rigorous foundations for parametrized homotopy theory, which is the
algebraic topology of spaces and spectra that are continuously parametrized by the points of …

Algebraic K-theory encodes important invariants for several mathematical disciplines,
spanning from geometric topology and functional analysis to number theory and algebraic …

Spectral Mackey functors are homotopy-coherent versions of ordinary Mackey functors as
defined by Dress. We show that they can be described as excisive functors on a suitable∞ …

Let G be a finite group and let F be a family of subgroups of G. We introduce a class of G-
equivariant spectra that we call F-nilpotent. This definition fits into the general theory of …

Equivariant homotopy theory started from geometrically motivated questions about
symmetries of manifolds. Several important equivariant phenomena occur not just for a …

We construct Quillen equivalences between the model categories of monoids (rings),
modules and algebras over two Quillen equivalent model categories under certain …