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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Tessellations of solvmanifolds


Author: Dave Witte
Journal: Trans. Amer. Math. Soc. 350 (1998), 3767-3796
MSC (1991): Primary 22E25, 22E40, 53C30; Secondary 05B45, 20G20, 20H15, 57S20, 57S30
MathSciNet review: 1432206
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Abstract: Let $A$ be a closed subgroup of a connected, solvable Lie group $G$, such that the homogeneous space $A\backslash G$ is simply connected. As a special case of a theorem of C. T. C. Wall, it is known that every tessellation $A\backslash G/\Gamma$ of $A\backslash G$ is finitely covered by a compact homogeneous space $G'/\Gamma'$. We prove that the covering map can be taken to be very well behaved - a ``crossed" affine map. This establishes a connection between the geometry of the tessellation and the geometry of the homogeneous space. In particular, we see that every geometrically-defined flow on $A\backslash G/\Gamma$ that has a dense orbit is covered by a natural flow on $G'/\Gamma'$.


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Additional Information

Dave Witte
Affiliation: Department of Mathematics, Williams College, Williamstown, MA 01267
Address at time of publication: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: dwitte@math.okstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01980-1
PII: S 0002-9947(98)01980-1
Received by editor(s): October 6, 1994
Received by editor(s) in revised form: November 5, 1996
Article copyright: © Copyright 1998 American Mathematical Society