Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

  • John D. Foley

This paper extends certain characterizations of nullhomotopic maps between p-compact groups to maps with target the p-completed classifying space of a connected Kac–Moody group and source the classifying space of either a p-compact group or a connected Kac–Moody group. A well known inductive principle for p-compact groups is applied to obtain general, mapping space level results. An arithmetic fiber square computation shows that a null map from the classifying space of a connected compact Lie group to the classifying space of a connected topological Kac–Moody group can be detected by restricting to the maximal torus. Null maps between the classifying spaces of connected topological Kac–Moody groups cannot, in general, be detected by restricting to the maximal torus due to the nonvanishing of an explicit abelian group of obstructions described here. Nevertheless, partial results are obtained via the application of algebraic discrete Morse theory to higher derived limit calculations. These partial results show that null maps are detected by restricting to the maximal torus in many cases of interest.

OriginalsprogEngelsk
TidsskriftMathematische Zeitschrift
Vol/bind301
Udgave nummer3
Sider (fra-til)2465-2496
ISSN0025-5874
DOI
StatusUdgivet - 2022

Bibliografisk note

Funding Information:
Supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92)

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

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