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

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Abstract

In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show that it gives rise to an isomorphism between higher twisted K-theory and higher twisted cohomology over the reals. Finally we compute spherical T-duality in higher twisted K-theory and higher twisted cohomology in very general cases.

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Acknowledgements

HS and VM were partially supported by funding from the Australian Research Council, through the Australian Laureate Fellowship FL170100020. LM and VM were partially supported by funding from the Australian Research Council, through the Discovery Project Grant DP200100729. HS wishes to acknowledge Jarah Evslin for useful discussions about spectral sequences and their differentials.

All three authors would like to thank the two anonymous referees for their comments on the paper, which have helped to improve the exposition.

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  1. School of Mathematical Sciences, University of Adelaide, Adelaide, 5005, Australia

    Lachlan Macdonald, Varghese Mathai & Hemanth Saratchandran

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  1. Lachlan Macdonald
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  2. Varghese Mathai
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  3. Hemanth Saratchandran
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Correspondence to Varghese Mathai.

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Macdonald, L., Mathai, V. & Saratchandran, H. On the Chern Character in Higher Twisted K-Theory and Spherical T-Duality. Commun. Math. Phys. 385, 331–368 (2021). https://doi.org/10.1007/s00220-021-04096-w

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