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By gluing together copies of an all right-angled Coxeter polytope a number of open hyperbolic $6$-manifolds with Euler characteristic $-1$ are constructed. They are the first known examples of hyperbolic $6$-manifolds having the smallest possible volume.

Copyright 2005 American Mathematical Society
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Article Info

• ERA Amer. Math. Soc. 11 (2005), pp. 40-46
• Publisher Identifier: S 1079-6762(05)00145-9
• 2000 Mathematics Subject Classification. Primary 57M50
• Received by editors October 31, 2004
• Posted on May 27, 2005
• Communicated by Walter Neumann
• Comments (When Available)

Brent Everitt

Department of Mathematics, University of York, York YO10 5DD, England

E-mail address: bje1@york.ac.uk

John Ratcliffe

Department of Mathematics, Vanderbilt University, Nashville, TN 37240

E-mail address: ratclifj@math.vanderbilt.edu

Steven Tschantz

Department of Mathematics, Vanderbilt University, Nashville, TN 37240

E-mail address: tschantz@math.vanderbilt.edu

The first author is grateful to the Mathematics Department, Vanderbilt University for its hospitality during a stay when the results of this paper were obtained.