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International Conference on Non-Positive Curvature in Group Theory, Topology, and Geometry
May 28-31, 1998
Vanderbilt University
Nashville, TN, USA

Organizers
B. Hughes, M. Mihalik, E. Prassidis, J. Ratcliffe, K. Ruane, M. Sapir, E. Schechter

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Deformaing Riemannian foliations and applications
by
T. Mark Kellum
Univ. Florida

Let (Mn, F0, < ·, · > ) be a compact, connected foliated manifold with dense leaves and equipped with a transverse holonomy invariant Riemannian metric tensor < ·, · > .

If either codim(F) < 5 or the isotropy Lie subalgebra of the structural Lie algebra of F0 is semisimple, then F0 is transversally homogeneous. The isotopy class of the transverse homogeneous structure of F0 and its global transverse holonomy homomorphism \rho0 in Hom(\pi1(Mn, x0), [G\tilde]) are simultaneously deformed yielding new Riemannian foliations F\rho of Mn, locally parametrized (up to an action by Ad(g)) by elements \rho' in Hom(\pi1(Mn, x0), [G\tilde]), for \rho' suffciently close to \rho0.

Date received: March 31, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabb-08.