arXiv: Experimental full text search
KT (K-theory)
Basic bundle theory etc, in K-theory folder.
arXiv:1008.4915 Motivic twisted K-theory from arXiv Front: math.AT by Markus Spitzweck, Paul Arne Østvær This paper sets out basic properties of motivic twisted K-theory with respect to degree three motivic cohomology classes of weight one. Motivic twisted K-theory is defined in terms of such motivic cohomology classes by taking pullbacks along the universal principal BG_m-bundle for the classifying space of the multiplicative group scheme. We show a Kuenneth isomorphism for homological motivic twisted K-groups computing the latter as a tensor product of K-groups over the K-theory of BG_m. The proof employs an Adams Hopf algebroid and a tri-graded Tor-spectral sequence for motivic twisted K-theory. By adopting the notion of an E-infinity ring spectrum to the motivic homotopy theoretic setting, we construct spectral sequences relating motivic (co)homology groups to twisted K-groups. It generalizes various spectral sequences computing the algebraic K-groups of schemes over fields. Moreover, we construct a Chern character between motivic twisted K-theory and twisted periodized rational motivic cohomology, and show that it is a rational isomorphism. The paper includes a discussion of some open problems.
http://ncatlab.org/nlab/show/twisted+K-theory
http://ncatlab.org/nlab/show/Karoubi+K-theory
arXiv:1002.3004 Twists of K-theory and TMF from arXiv Front: math.AT by Matthew Ando, Andrew J. Blumberg, David Gepner We explore an approach to twisted generalized cohomology from the point of view of stable homotopy theory and quasicategory theory provided by arXiv:0810.4535. We explain the relationship to the twisted K-theory provided by Fredholm bundles. We show how our approach allows us to twist elliptic cohomology by degree four classes, and more generally by maps to the four-stage Postnikov system BO0...4>. We also discuss Poincare duality and umkehr maps in this setting.
arXiv:1001.4790 A universal coefficient theorem for twisted K-theory from arXiv Front: math.AT by Mehdi Khorami 1 person liked this In this paper, we recall the definition of twisted K-theory in various settings. We prove that for a twist corresponding to a three dimensional integral cohomology class of a space X, there exist a “universal coefficient” isomorphism K_{}^{\tau}(X)\cong K_{}(P_{\tau})\otimes_{K_{}(\mathbb{C}P^{\infty})} \hat{K}_{} where is the total space of the principal -bundle induced over X by and is obtained form the action of on K-theory.
nLab page on Twisted K-theory