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 …

Some recent advances in topological Hochschild homology - Mathew - 2022 - Bulletin of the
London Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article …

We formulate differential cohomology and Chern-Weil theory--the theory of connections on
fiber bundles and of gauge fields--abstractly in the context of a certain class of higher …

In this work we present a new approach to the theory of noncommutative motives and use it
to explain the different flavors of algebraic K-theory of schemes and dg-categories. The work …

We establish a canonical and unique tensor product for commutative monoids and groups in
an∞–category C which generalizes the ordinary tensor product of abelian groups. Using …

We apply the mechanism of factorization homology to construct and compute category‐
valued two‐dimensional topological field theories associated to braided tensor categories …

We study the étale sheafification of algebraic K-theory, called étale K-theory. Our main
results show that étale K-theory is very close to a noncommutative invariant called Selmer K …

To a “stable homotopy theory”(a presentable, symmetric monoidal stable∞-category), we
naturally associate a category of finite étale algebra objects and, using Grothendieck's …

To any pullback square of ring spectra we associate a new ring spectrum and use it to
describe the failure of excision in algebraic K-theory. The construction of this new ring …

We define Grothendieck-Witt spectra in the setting of Poincaré-categories and show that
they fit into an extension with a K-and an L-theoretic part. As consequences, we deduce …