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28 March 2024
 
  » arxiv » math.AT/0306027

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Two-vector bundles and forms of elliptic cohomology
Nils A. Baas ; Bj{o}rn Ian Dundas ; John Rognes ;
Date 2 Jun 2003
Journal London Math. Soc. Lecture Note Ser., 308, Cambridge Univ. Press, Cambridge, 2004.
Subject Algebraic Topology; K-Theory and Homology; Mathematical Physics MSC-class: 55R65 (Primary) 18D05, 19D99 (Secondary) | math.AT math-ph math.KT math.MP
AbstractIn this paper we define 2-vector bundles as suitable bundles of 2-vector spaces over a base space, and compare the resulting 2-K-theory with the algebraic K-theory spectrum K(V) of the 2-category of 2-vector spaces, as well as the algebraic K-theory spectrum K(ku) of the connective topological K-theory spectrum ku. We explain how K(ku) detects v_2-periodic phenomena in stable homotopy theory, and as such is a form of elliptic cohomology.
Source arXiv, math.AT/0306027
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