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A note on the double quaternionic transfer and its $ f$-invariant

Author: Hanno von Bodecker
Journal: Proc. Amer. Math. Soc. 144 (2016), 2731-2740
MSC (2010): Primary 55Q45; Secondary 55R25, 58J26
Published electronically: November 4, 2015
MathSciNet review: 3477091
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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.

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Additional 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
Article copyright: © Copyright 2015 American Mathematical Society

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