Line bundle twists for unitary bordism are ghosts

Hertl, Thorsten¹

¹School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia

Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2053-2066

Résumé

We prove that the canonical twist ζ : K(ℤ,3) → BGL ⁡ 1(MSpin ⁡ c) does not extend to a twist for unitary bordism by showing that every continuous map f : K(ℤ,3) → BGL ⁡ 1(MU) loops to a nullhomotopic map.

Détail

DOI : 10.2140/agt.2025.25.2053

Keywords: bordism theory, twisted homology theory, classifying spaces

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