A note on the double quaternionic transfer and its $f$–invariant
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- by Hanno von Bodecker
- Proc. Amer. Math. Soc. 144 (2016), 2731-2740
- DOI: https://doi.org/10.1090/proc/12940
- Published electronically: November 4, 2015
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Abstract:
It is well known that for a line bundle over a closed framed manifold, its sphere bundle can also be given the structure of a framed manifold, usually referred to as a transfer. Given a pair of lines, the procedure can be generalized to obtain a double transfer. We study the quaternionic case, and derive a simple formula for the $f$–invariant of the underlying bordism class, enabling us to investigate its status in the Adams–Novikov spectral sequence. As an application, we treat the situation of quaternionic flag manifolds.References
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Bibliographic Information
- Hanno von Bodecker
- Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
- Received by editor(s): June 1, 2015
- Received by editor(s) in revised form: August 8, 2015
- Published electronically: November 4, 2015
- Communicated by: Michael A. Mandell
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2731-2740
- MSC (2010): Primary 55Q45; Secondary 55R25, 58J26
- DOI: https://doi.org/10.1090/proc/12940
- MathSciNet review: 3477091