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On the regular genus of 5-manifolds with free fundamental group

On the regular genus of 5-manifolds with free fundamental group Abstract. In the present paper, we obtain the following classification of closed orientable PL 5manifolds M 5 with free fundamental group of rank m, so that the di¤erence between the regular genus GðM 5 Þ and m is less or equal to eight: (a) GðM 5 Þ ¼ m i¤ M 5 G am ðS 1 Â S 4 Þ; (b) it is impossible m þ 1 a GðM 5 Þ a m þ 7; (c) if GðM 5 Þ ¼ m þ 8, then either M 5 G am ðS 1 Â S 4 ÞaðS 2 Â S 3 Þ or M 5 G am ðS 1 Â S 4 ÞaðS 2 Â S 3 Þ. @ As a consequence, we complete the classification of PL 5-manifolds up to regular genus eight, and compute the regular genus of the 5-dimensional real projective space RP 5 : if GðM 5 Þ ¼ 8; M 5 G S2 Â S3 @ GðS 2 Â S 3 Þ ¼ 8; then either M 5 G S2 Â S3 or or M 5 G a8 ðS 1 Â S 4 Þ; GðS 2 Â S 3 Þ b 8; @ GðRP http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

On the regular genus of 5-manifolds with free fundamental group

Casali, Maria Rita
Forum Mathematicum , Volume 15 (3) – May 20, 2003
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Publisher
de Gruyter
Copyright
Copyright © 2003 by Walter de Gruyter GmbH & Co. KG
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.2003.025
Publisher site
See Article on Publisher Site

Abstract

Abstract. In the present paper, we obtain the following classification of closed orientable PL 5manifolds M 5 with free fundamental group of rank m, so that the di¤erence between the regular genus GðM 5 Þ and m is less or equal to eight: (a) GðM 5 Þ ¼ m i¤ M 5 G am ðS 1 Â S 4 Þ; (b) it is impossible m þ 1 a GðM 5 Þ a m þ 7; (c) if GðM 5 Þ ¼ m þ 8, then either M 5 G am ðS 1 Â S 4 ÞaðS 2 Â S 3 Þ or M 5 G am ðS 1 Â S 4 ÞaðS 2 Â S 3 Þ. @ As a consequence, we complete the classification of PL 5-manifolds up to regular genus eight, and compute the regular genus of the 5-dimensional real projective space RP 5 : if GðM 5 Þ ¼ 8; M 5 G S2 Â S3 @ GðS 2 Â S 3 Þ ¼ 8; then either M 5 G S2 Â S3 or or M 5 G a8 ðS 1 Â S 4 Þ; GðS 2 Â S 3 Þ b 8; @ GðRP

Journal

Forum Mathematicum – de Gruyter

Published: May 20, 2003

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