A note on the double quaternionic transfer and its f-invariant
Algebraic Topology
2014-12-19 v2 Geometric Topology
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.
Cite
@article{arxiv.1103.6151,
title = {A note on the double quaternionic transfer and its f-invariant},
author = {Hanno von Bodecker},
journal= {arXiv preprint arXiv:1103.6151},
year = {2014}
}
Comments
13 pages. Generalized the proof (and the statement) of the main theorem to hold at any level N>1; also added a remark on a specific framing of the flag manifolds