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

@article{Macdonald2020OnTC,
  title={On the Chern Character in Higher Twisted K-Theory and Spherical T-Duality},
  author={Lachlan Macdonald and Varghese Mathai and Hemanth Saratchandran},
  journal={arXiv: Differential Geometry},
  year={2020}
}
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. 
Computations in higher twisted $K$-theory
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 giveExpand

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