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

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.

arXiv comment13 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