On the Chern Character in Higher Twisted K-Theory and Spherical T-Duality

MacDonald, Lachlan; Mathai, Varghese; Saratchandran, Hemanth

doi:10.1007/s00220-021-04096-w

Cited by 2 publications

(2 citation statements)

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“…Atiyah and Segal are also able to show in [6] that the higher differentials of the spectral sequence for classical twisted K-theory are given rationally by higher Massey products, and they do so by generalising the Chern character to the twisted setting. This work can likely be generalised to the higher twisted setting, and in fact the Chern character has already been generalised to this setting [40], but since it only gives the differentials rationally it is not highly applicable to computations.…”

Section: Spectral Sequencesmentioning

confidence: 99%

“…Further work in studying higher twisted K-theory in relation to spherical T-duality is done by MacDonald, Mathai and Saratchandran [40], who also develop a Chern character in higher twisted K-theory and give an isomorphism between higher twisted K-theory and higher twisted cohomology over the reals.…”

Section: Introduction Background Higher Twists Links With Physics Mai...mentioning

confidence: 99%

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Computations in higher twisted $K$-theory

Brook¹

2020

Preprint

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Higher twisted K-theory is an extension of twisted K-theory introduced by Ulrich Pennig which captures all of the homotopy-theoretic twists of topological K-theory in a geometric way. We give an overview of his formulation and key results, and reformulate the definition from a topological perspective. We then investigate ways of producing explicit geometric representatives of the higher twists of K-theory viewed as cohomology classes in special cases using the clutching construction and when the class is decomposable. Atiyah-Hirzebruch and Serre spectral sequences are developed and information on their differentials is obtained, and these along with a Mayer-Vietoris sequence in higher twisted K-theory are applied in order to perform computations for a variety of spaces.

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Section: Spectral Sequencesmentioning

confidence: 99%

Section: Introduction Background Higher Twists Links With Physics Mai...mentioning

confidence: 99%