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result(s) for
"K-theory."
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Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories
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(*).
eBook
The politics of Harry Potter
\"This political analysis of Harry Potter uses the beloved wizarding world to introduce readers to the equally murky and intimidating world of the political. Readers may be surprised to discover that in fact J.K. Rowling's work provides us with entries into all of the most important political questions in history - from current controversies about terrorism and human rights, to the classic foundations of political thought\"-- Provided by publisher.
BOOK
On the K-theory of pullbacks
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.
Journal Article
Reset : my fight for inclusion and lasting change
The co-founder of the diversity nonprofit Project Include shares the story behind her landmark 2015 lawsuit against powerhouse venture capitalist firm Kleiner Perkins, exploring what her case and refusal to settle revealed about Silicon Valley discrimination.
Book
Witten Non Abelian Localization for Equivariant K-Theory, and the 𝑄,𝑅=0 Theorem
The purpose of the present memoir is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional
compact manifold : following an idea of E. Witten, we deform an elliptic symbol associated to a Clifford bundle on M with a vector field
associated to a moment map. Second, we use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar in the
Hamiltonian case, and we obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to
obtain a geometric description of the multiplicities of the index of general
eBook
Noncommutative geometry and global analysis : conference in honor of Henri Moscovici, June 29-July 4, 2009, Bonn, Germany
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.
eBook
Nonarchimedean bivariant$K$ -theory
We introduce bivariant K -theory for nonarchimedean bornological algebras over a complete discrete valuation ring V . This is the universal target for dagger homotopy invariant, matrically stable, and excisive functors, similar to bivariant K -theory for locally convex topological C -algebras and algebraic bivariant K -theory. As in the archimedean case, we use the universal property to construct a bivariant Chern character into analytic and periodic cyclic homology. When the first variable is the ground algebra V , we get a version of Weibel’s homotopy algebraic K -theory, which we call stabilised overconvergent analytic K -theory . The resulting analytic K -theory satisfies dagger homotopy invariance, stability by completed matrix algebras, and excision.
Journal Article
Expanders are counterexamples to the l.sup.p coarse Baum-Connes conjecture
We consider an [l.sup.p] coarse Baum-Connes assembly map for 1 < p < [infinity], and show that it is not surjective for expanders arising from residually finite hyperbolic groups. Keywords. K-theory, [l.sup.p] coarse Baum-Connes conjecture, coarse geometry.
Journal Article
K-theory of valuation rings
We prove several results showing that the algebraic $K$-theory of valuation rings behaves as though such rings were regular Noetherian, in particular an analogue of the Geisser–Levine theorem. We also give some new proofs of known results concerning cdh descent of algebraic $K$-theory.
Journal Article