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Families of SU(2) representations for mapping cylinders of periodic monodromy

Published online by Cambridge University Press:  20 January 2009

G. Daskalopoulos ,
S. Dostoglou  and
R. Wentworth
G. Daskalopoulos
Affiliation:
Department of Mathematics, Brown University, Providence, RI 02912, U.S.A.
S. Dostoglou
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.
R. Wentworth
Affiliation:
Department of Mathematics, University of California at Irvine, Irvine, CA 92717, U.S.A.
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Abstract

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We examine the action of diffeomorphisms of an oriented surface with boundary on the space of conjugacy classes of SU(2) representations of the fundamental group and prove that in the case of a single periodic diffeomorphism the induced action always has fixed points. For the corresponding 3-dimensional mapping cylinders we obtain families of representations parametrized by their value on the longitude of the torus boundary.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 2 , June 1997 , pp. 383 - 392
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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