Twisted K-Theory and K-Theory of Bundle Gerbes

By P. Bouwknegt, Alan L. Carey, Varghese Mathai, Michael K. Murray, Danny Stevenson. 2001

295 citations recorded by the source corpus.

Abstract: In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of K-brane charges in nontrivial backgrounds are briefly discussed.

Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/549b83f832c1cb6574270e080518619ffec5a6a7

How researchers see this paper

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In Astronomy and Astrophysics

1. N. Seiberg
2. G. Moore
3. J. Maldacena
4. E. Witten
5. D. Freed
6. M. Hopkins
7. C. Teleman
8. P. Bouwknegt

In Mathematical Physics

1. G. Moore
2. D. Freed
3. M. Hopkins
4. C. Teleman
5. G. Segal
6. Urs Schreiber
7. N. Seiberg
8. J. Maldacena

In Nuclear and High Energy Physics

1. G. Moore
2. N. Seiberg
3. E. Witten
4. D. Freed
5. J. Maldacena
6. M. Hopkins
7. C. Teleman
8. P. Bouwknegt

Citations in the corpus

• WZW BRANES AND GERBES (2002, unknown): “ ⊔ i,j′,l′ Oijl ×C . ∼ (C.7) over SU(N), where the equivalence relation ∼ is defined by (g,ζ1,i1j1l1) ∼ (g,ζ2,i2j2l2) if ζ1 = ζ2 χ kλ l′ 1 l′ 2 (wb w−1 a w −1 [b−a]). (C.8) 46 For (y,y′,y′′,y′′′) ∈ Y[4] Γ with y′′′ = (z−1 cg,n ′), n= [n′ + c] and γ3 = z−1 b z, the isomorphism (5.10) identifies [g,ζ,ij”
• Twisted equivariant K‐theory with complex coefficients (2002, methodology): “) For torsion, non-equivariant twistings, the relevant K-theory was first introduced in [14]; subsequent treatments ([28] and, more recently, [1, 5, 8]) remove the torsion assumption.”
• Twisted K-theory (2004, background): “Many papers have appeared recently discussing twisted K-theory in relation to string theory, the most comprehensive probably being that of the Adelaide school [6].”
• D branes on group manifolds and fusion rings (2002, methodology): “A particularly concrete presentation of twisted K-theory is as the Grothendieck K-theory of (isomorphism classes of) bundle gerbe modules [38].”
• Loop groups and twisted K‐theory I (2007, methodology): “In addition to [3] we refer the reader to [ 10 , 33].”
• Twisted Differential String and Fivebrane Structures (2009, background): “PU(k)bundles and the corresponding twisted U(k)-bundles model the Chan-Paton bundles on D-branes and give classes in twisted K-theory [89] [49] [20] [19].”
• D-Brane Instantons and K-Theory Charges (2001, background): “Institute for Advanced Study Einstein Drive Princeton, New Jersey, 08540”
• Principal ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\infty $$\end{document}-bundles: general theory (2012, methodology): “Under this identification the∞-bundle classified by the obstruction class [c(gX )] above is what is called the lifting bundle gerbe of the lifting problem, see for instance [4] for a review.”
• T-Duality: Topology Change from H-Flux (2003, methodology): “Twisted cohomology has been studied in detail in the papers [22, 23].”
• What is geometry in quantum theory (2004, background): “One also meets the Dixmier–Douady class as the obstruction to a bundle gerbe being trivial [78].”