Cut numbers of -manifolds

Author:
Adam S. Sikora

Journal:
Trans. Amer. Math. Soc. **357** (2005), 2007-2020

MSC (2000):
Primary 57M05, 57M27, 20F34, 11E76

DOI:
https://doi.org/10.1090/S0002-9947-04-03581-0

Published electronically:
October 7, 2004

MathSciNet review:
2115088

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Abstract: We investigate the relations between the cut number, and the first Betti number, of -manifolds We prove that the cut number of a ``generic'' -manifold is at most This is a rather unexpected result since specific examples of -manifolds with large and are hard to construct. We also prove that for any complex semisimple Lie algebra there exists a -manifold with and Such manifolds can be explicitly constructed.

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Additional Information

**Adam S. Sikora**

Affiliation:
Department of Mathematics, 244 Mathematics Building, SUNY at Buffalo, Buffalo, New York 14260

Email:
asikora@buffalo.edu

DOI:
https://doi.org/10.1090/S0002-9947-04-03581-0

Keywords:
Cut number,
3-manifold,
corank,
skew-symmetric form,
cohomology ring

Received by editor(s):
October 28, 2002

Received by editor(s) in revised form:
December 2, 2003

Published electronically:
October 7, 2004

Article copyright:
© Copyright 2004
American Mathematical Society