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EXAMPLES OF NON-HOMEOMORPHIC HARMONIC MAPS BETWEEN NEGATIVELY CURVED MANIFOLDS

Published online by Cambridge University Press:  01 May 1998

F. T. FARRELL ,
L. E. JONES  and
P. ONTANEDA
F. T. FARRELL
Affiliation:
Department of Mathematical Sciences, State University of New York, Binghampton, NY 13902, USA
L. E. JONES
Affiliation:
Max Plank Institute, Gottfried-Claren-Strasse 26, 53225 Bonn, Germany
P. ONTANEDA
Affiliation:
Department of Mathematical Sciences, State University of New York, Stony Brook, NY 11794, USA
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Abstract

Let M and N be closed non-positively curved manifolds, and let f[ratio ]M→N be a smooth map. Results of Eells and Sampson [1] show that f is homotopic to a harmonic map ϕ, and Hartman [6] showed that this ϕ is unique when N is negatively curved and f∗(π1 M) is not cyclic. Lawson and Yau conjectured that if f[ratio ]M→N is a homotopy equivalence, where M and N are negatively curved, then the unique harmonic map ϕ homotopic to f would be a diffeomorphism. Counterexamples to this conjecture appeared in [2], and later in [7] and [5].

There remains the question of whether a ‘topological’ Lawson–Yau conjecture holds.

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Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 3 , May 1998 , pp. 295 - 296
Copyright
© The London Mathematical Society 1998

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