English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Preprint

Symmetries of exotic spheres via complex and quaternionic Mahowald invariants

MPS-Authors
/persons/resource/persons289556

Quigley,  J. D.
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)

2309.04275.pdf
(Preprint), 269KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Botvinnik, B., & Quigley, J. D. (submitted). Symmetries of exotic spheres via complex and quaternionic Mahowald invariants.


Cite as: https://hdl.handle.net/21.11116/0000-000F-5E1B-B
Abstract
We deduce the existence of smooth U(1)- and Sp(1)-actions on certain exotic spheres using complex and quaternionic analogues of the Mahowald {(root)} invariant. In particular, we prove that the complex (respectively, quaternionic) Mahowald invariant takes an element of πsk represented by a homotopy sphere Σk to an element {of πk+ℓ} represented by another homotopy sphere Σk+ℓ equipped with a smooth U(1)- (respectively, Sp(1)-) action with fixed points the original homotopy sphere Σk⊂Σk+ℓ. This work is motivated by results of Stolz on the classical Mahowald invariant and smooth C2-actions on homotopy spheres.