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

Since its introduction by Friedhelm Waldhausen in the 1970s, the algebraic K-theory of
spaces has been recognized as the main tool for studying parametrized phenomena in the …

We construct the strong weight complex functor for a stable infinity-category C equipped with
a bounded weight structure w. Along the way we prove that C is determined by the …

The topological Hochschild homology THH (R) of a commutative S–algebra (E∞ ring
spectrum) R naturally has the structure of a commutative R–algebra in the strict sense, and …

A logarithmic structure on a commutative ring A is a commutative monoid M with a
homomorphism to the underlying multiplicative monoid of A. This determines a localization …

We give a new formula for $ p $-typical real topological cyclic homology that refines the fiber
sequence formula discovered by Nikolaus and Scholze for $ p $-typical topological cyclic …

We describe a construction of the cyclotomic structure on topological Hochschild homology
(THH) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis …

This book explores string topology, Hochschild and cyclic homology, assembling material
from a wide scattering of scholarly sources in a single practical volume. The first part offers a …

We show that if we factor the long exact sequence in cohomology of a cofiber sequence of
spectra into short exact sequences, then the $ d_2 $-differential in the Adams spectral …

For any compact Lie group $ G $, we give a description of genuine $ G $-spectra in terms of
the naive equivariant spectra underlying their geometric fixedpoints. We use this to give an …