Classifying PL -manifolds up to regular genus seven

Authors:
Maria Rita Casali and Carlo Gagliardi

Journal:
Proc. Amer. Math. Soc. **120** (1994), 275-283

MSC:
Primary 57Q99

MathSciNet review:
1205484

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Abstract: In the present paper, we show that the only closed orientable -manifolds of regular genus less or equal than seven are the -sphere and the connected sums of copies of , with . As a consequence, the genus of is proved to be eight. This suggests a possible approach to the (-dimensional) Poincaré Conjecture, via the well-known classification of simply connected -manifolds, obtained by Smale and Barden.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1205484-4

Keywords:
-Manifolds,
regular genus,
classification,
products of spheres and manifolds,
handlebodies,
Poincaré Conjecture,
edge-coloured graphs,
-cell embeddings

Article copyright:
© Copyright 1994
American Mathematical Society