Volume 11, issue 2 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Spindle-configurations of skew lines

Roland Bacher and David Garber

Geometry & Topology 11 (2007) 1049–1081

arXiv: math.GT/0205245

Abstract

This paper is a contribution to the classification of configurations of skew lines, as studied mainly by Viro and his collaborators. We prove an improvement of a conjecture made by Crapo and Penne which characterizes isotopy classes of skew configurations with spindle-structure. By this result we can define an invariant, spindlegenus, for spindle-configurations.

Keywords
configurations of skew lines, spindles, linking matrix, switching graphs, permutation
Mathematical Subject Classification 2000
Primary: 57M25, 57Q37, 57Q45
Secondary: 51H10, 57M27
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Publication
Received: 29 September 2005
Revised: 14 November 2006
Accepted: 2 January 2007
Published: 30 May 2007
Proposed: Dave Gabai
Seconded: Joan Birman and Jean-Pierre Otal
Authors
Roland Bacher
Institut Fourier
BP 74 38402 Saint-Martin D’Heres Cedex
France
David Garber
Department of Applied Mathematics
School of Sciences
Holon Institute of Technology
52 Golomb Street
PO Box 305
58102 Holon
Israel