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 …

The stable homotopy category, much studied by algebraic topologists, is a closed symmetric
monoidal category. For many years, however, there has been no well-behaved closed …

In recent years the theory of structured ring spectra (formerly known as A-and E-ring spectra)
has been simplified by the discovery of categories of spectra with strictly associative and …

Axiomatic homotopy theory for operads Page 1 Comment. Math. Helv. 78 (2003) 805–831
0010-2571/03/040805-27 DOI 10.1007/s00014-003-0772-y c© 2003 Birkhäuser Verlag, Basel …

The last few years have seen a revolution in our understanding of the foundations of stable
homotopy theory. Many symmetric monoidal model categories of spectra whose homotopy …

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 …

We give two general constructions for the passage from unstable to stable homotopy that
apply to the known example of topological spaces, but also to new situations, such as the A …

Let E be a homotopy commutative ring spectrum, and suppose the ring of cooperations E∗ E
is flat over E∗. We wish to address the following question: given a commutative E∗-algebra …

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