Morse theory and infinite families of harmonic maps between spheres

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dc.creatorCorlette, Kevin
dc.creatorWald, Robert M.
dc.date1999-12-01
dc.date1999-12-02
dc.date.accessioned2026-07-07T04:33:07Z
dc.date.available2026-07-07T04:33:07Z
dc.descriptionExistence of an infinite sequence of harmonic maps between spheres of certain dimensions was proven by Bizon and Chmaj. This sequence shares many features of the Bartnik-McKinnon sequence of solutions to the Einstein-Yang-Mills equations as well as sequences of solutions that have arisen in other physical models. We apply Morse theory methods to prove existence of the harmonic map sequence and to prove certain index and convergence properties of this sequence. In addition, we generalize the result of Bizon and Chmaj to produce infinite sequences of harmonic maps not previously known. The key features ``responsible'' for the existence and properties of these sequences are thereby seen to be the presence of a reflection symmetry and the existence of a singular harmonic map of infinite index which is invariant under this symmetry.
dc.description17 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math-ph/9912001
dc.identifierhttp://arxiv.org/abs/math-ph/9912001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58456
dc.subjectMathematical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.subject58E20; 83C20
dc.titleMorse theory and infinite families of harmonic maps between spheres
dc.typetext

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