University of Sussex
Browse

File(s) under permanent embargo

Spherical twists, SO(n) and the lifting of their twist paths to Spin(n) in low dimensions

journal contribution
posted on 2023-06-09, 08:40 authored by Ali TaheriAli Taheri
Let X ? Rn be a generalized annulus and consider the Dirichlet energy functional E[u;X] := 1/2?x|?u(x)|²dx, on the set of admissible maps A?(X) = {u?W²,¹(X, Sn¯¹): u|?X = ?}. Here ? ? C(?X, Sn¯¹) is fixed and A?(X) is non-empty. In this paper, we consider a class of maps referred to as spherical twists and examine them in connection with the Euler–Lagrange equation associated with E[·, X] on A?(X) (the harmonic map equation on X). The approach is novel and is based on lifting twist paths from SO(n) to its double cover Spin(n) and reformulating the harmonic map equation accordingly. We prove that, for n = 4 depending on ?, the system admits infinitely many smooth solutions in the form of twists or none, whereas, for n = 3 and in contrast, this number severely reduces to one or none.

History

Publication status

  • Published

File Version

  • Published version

Journal

Quarterly Journal of Mathematics

ISSN

0033-5606

Publisher

Oxford University Press

Issue

3

Volume

63

Page range

723-751

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2017-11-07

First Compliant Deposit (FCD) Date

2017-11-06

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC