This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16-20, 2018, in La Plata, Argentina, and the ...workshop was held from July 23-27, 2018, in Buenos Aires, Argentina. The volume showcases current developments in K-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections. Papers cover topics such as K-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative K-groups of monoid algebras, Milnor K-theory and regulators, noncommutative motives, the classification of C^*-algebras via Kasparov's K-theory, the comparison between full and reduced C^*-crossed products, and a proof of Bott periodicity using almost commuting matrices.
This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics ...such as category theory and homological algebra, functor homology, algebraic K -theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.
The authors develop a theory of THH and TC of Waldhausen categories and prove the analogues of Waldhausen's theorems for K-theory. They resolve the longstanding confusion about localization sequences ...in THH and TC, and establish a specialized dévissage theorem. As applications, the authors prove conjectures of Hesselholt and Ausoni-Rognes about localization cofiber sequences surrounding THH(ku), and more generally establish a framework for advancing the Rognes program for studying Waldhausen's chromatic filtration on A(*).
This volume represents the proceedings of the conference on Noncommutative Geometric Methods in Global Analysis, held in honor of Henri Moscovici, from June 29-July 4, 2009, in Bonn, Germany. Henri ...Moscovici has made a number of major contributions to noncommutative geometry, global analysis, and representation theory. This volume, which includes articles by some of the leading experts in these fields, provides a panoramic view of the interactions of noncommutative geometry with a variety of areas of mathematics. It focuses on geometry, analysis and topology of manifolds and singular spaces, index theory, group representation theory, connections of noncommutative geometry with number theory and arithmetic geometry, Hopf algebras and their cyclic cohomology.
This volume contains the proceedings of the conference on Manifolds, $K$-Theory, and Related Topics, held from June 23-27, 2014, in Dubrovnik, Croatia.The articles contained in this volume are a ...collection of research papers featuring recent advances in homotopy theory, $K$-theory, and their applications to manifolds. Topics covered include homotopy and manifold calculus, structured spectra, and their applications to group theory and the geometry of manifolds.This volume is a tribute to the influence of Tom Goodwillie in these fields.
On the K-theory of pullbacks Land, Markus; Tamme, Georg
Annals of mathematics,
11/2019, Letnik:
190, Številka:
3
Journal Article
Odprti dostop
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 spectrum is categorical ...and hence allows us to determine the failure of excision for any localizing invariant in place of K-theory.
As immediate consequences we obtain an improved version of Suslin's excision result in K-theory, generalizations of results of Geisser and Hesselholt on torsion in (bi)relative K-groups, and a generalized version of proexcision for K-theory. Furthermore, we show that any truncating invariant satisfies excision, nilinvariance, and cdh-descent. Examples of truncating invariants include the fibre of the cyclotomic trace, the fibre of the rational Goodwillie–Jones Chern character, periodic cyclic homology in characteristic zero, and homotopy K-theory.
Various of the results we obtain have been known previously, though most of them in weaker forms and with less direct proofs.
We show that the Gersten complex for the (improved) Milnor K-sheaf on a smooth scheme over an excellent discrete valuation ring is exact except at the first place and that exactness at the first ...place may be checked at the discrete valuation ring associated to the generic point of the special fibre. This complements results of Gillet-Levine for K-theory, Geisser for motivic cohomology and Schmidt-Strunk and the author for étale cohomology.
We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are finitely ...generated. For polynomial functors, we study also a weaker homological finiteness property, which applies to twisted homological stability for matrix monoids. This is inspired by works by Schwartz and Betley-Pirashvili, which are generalised; this also uses decompositions à la Steinberg over an additive category that we recently got with Vespa. We show also, as an application, a finiteness property for stable homology of linear groups on suitable rings.
Nous donnons des conditions suffisantes pour qu'un foncteur de longueur finie d'une catégorie additive vers des espaces vectoriels de dimensions finies possède une résolution projective dont les termes sont de type fini. Pour les foncteurs polynomiaux, nous étudions également une propriété de finitude homologique plus faible, qui s'applique à la stabilité homologique à coefficients tordus des monoïdes de matrices. Ces résultats s'inspirent de travaux de Schwartz et Betley-Pirashvili, qu'ils généralisent, et utilisent les théorèmes de décomposition à la Steinberg que nous avons récemment obtenus avec Vespa. Nous montrons également, en guise d'application, une propriété de finitude pour l'homologie stable de groupes linéaires sur des anneaux appropriés.
The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can ...be efficiently approximated using numerical methods, but this only is possible in low dimensional example. In this paper we examine the higher-dimensional spheres that can arise from theoretical examples. We also describe a constructive method to generate five real symmetric almost commuting matrices that have a K-theoretical obstruction to being close to commuting matrices. For this, we look to matrix models of topological electric circuits.
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