Two-vector bundles and forms of elliptic cohomology

Baas, Nils A.; Dundas, Bjørn Ian; Rognes, John

doi:10.1017/cbo9780511526398.005

Cited by 67 publications

(65 citation statements)

References 23 publications

(13 reference statements)

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“…For example, one could argue that K-theory of K-theory should also be considered a twisting of K-theory. This was calculated by Baas-Dundas-Rognes [44], and shown to be related to elliptic cohomology, which we will consider in the next section.…”

Section: Even More General Twisted K-theory?mentioning

confidence: 98%

Type IIB string theory, S-duality, and generalized cohomology

Kříž

Sati

2005

Nuclear Physics B

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In the presence of background Neveu-Schwarz flux, the description of the Ramond-Ramond fields of type IIB string theory using twisted K-theory is not compatible with S-duality. We argue that other possible variants of twisted K-theory would still not resolve this issue. We propose instead a connection of S-duality with elliptic cohomology, and a possible T-duality relation of this to a previous proposal for IIA theory, and higher-dimensional limits. In the process, we obtain some other results which may be interesting on their own. In particular, we prove a conjecture of Witten that the 11-dimensional spin cobordism group vanishes on K(Z, 6), which eliminates a potential new θ-angle in type IIB string theory.

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Section: Even More General Twisted K-theory?mentioning

confidence: 98%

Type IIB string theory, S-duality, and generalized cohomology

Kříž

Sati

2005

Nuclear Physics B

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“…the category Vect(H) of finite dimensional vector spaces in H. From the view point of stable homotopy theory, the (co)homology theory next to K-theory is the elliptic (co)homology theory. There is an attempt by Baas, Dundas and Rognes [BDR04] to define a form of elliptic cohomology theory by using a categorification of Vect(H).…”

Section: It Is Essentially Proved By Madsen and Tillmann That The Incmentioning

confidence: 99%

Two-Sided Bar Constructions for Partial Monoids and Applications to K-Homology Theory

Tamaki

2013

Noncommutative Geometry and Physics 3

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“…While defining tmf is a subtle process, informally tmf is the universal elliptic cohomology theory, or the elliptic cohomology theory associated to the universal moduli stack of elliptic curves. Despite several attempts [Baas et al 2004;Hu and Kriz 2004;Segal 1988;Stolz and Teichner 2004], there is still no geometric description of tmf. However, it is believed that tmf should provide a natural home for family index theorems on loop spaces.…”

Section: ‫ޚ‬mentioning

confidence: 99%

String structures and canonical 3-forms

Redden¹

2011

Pacific J. Math.

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Using basic homotopy constructions, we show that isomorphism classes of string structures on spin bundles are naturally given by certain degree 3 cohomology classes, which we call string classes, on the total space of the bundle. Using a Hodge isomorphism, we then show that the harmonic representative of a string class gives rise to a canonical 3-form on the base space, refining the associated differential character. We explicitly calculate this 3-form for homogeneous metrics on 3-spheres, and we discuss how the cohomology theory tmf could potentially encode obstructions to positive Ricci curvature metrics.

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Two-vector bundles and forms of elliptic cohomology

Cited by 67 publications

References 23 publications

Type IIB string theory, S-duality, and generalized cohomology

Type IIB string theory, S-duality, and generalized cohomology

Two-Sided Bar Constructions for Partial Monoids and Applications to K-Homology Theory

String structures and canonical 3-forms

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