Some graph-theoretical tools are used to introduce the concept of regular genus, for every closed, n-dimensional PL manifold M^n. Then it is proved that the regular genus of every surface equals its genus, and that the regular genus of every 3-manifold M^3 equals its Heegaard genus if M^3 is orientable, and twice its Heegaard genus if M^3 is non orientable. A geometric opproach and some applications in dimension 4 are also presented.
Extending the concept of genus to dimension n / Gagliardi, Carlo. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 81:(1981), pp. 473-481.
Extending the concept of genus to dimension n
GAGLIARDI, Carlo
1981
Abstract
Some graph-theoretical tools are used to introduce the concept of regular genus, for every closed, n-dimensional PL manifold M^n. Then it is proved that the regular genus of every surface equals its genus, and that the regular genus of every 3-manifold M^3 equals its Heegaard genus if M^3 is orientable, and twice its Heegaard genus if M^3 is non orientable. A geometric opproach and some applications in dimension 4 are also presented.
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