In the present paper the classification of PL 4-manifolds by means of the combinatorial invariant “regular genus” is proved to be not finite to one: indeed, the set of all $D^2$-bundles over $S^2$ (i.e. every bundle $\csi_c$ with Euler class $c$ and boundary L(c,1), $c \in Z-\{0,-1,-1}$, together with the trivial bundle $S^2 X D^2$) constitutes an infinite family of PL 4-manifolds with the same regular genus (equal to three). Further, general results are obtained, concerning PL 4-manifolds with “restricted gap” between their regular genus and the rank of their fundamental group, especially in case of free fundamental group.

An infinite class of bounded 4-manifolds having regular genus three / Casali, Maria Rita. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. A. - ISSN 0392-4033. - STAMPA. - 10:(1996), pp. 279-303.

An infinite class of bounded 4-manifolds having regular genus three

CASALI, Maria Rita
1996

Abstract

In the present paper the classification of PL 4-manifolds by means of the combinatorial invariant “regular genus” is proved to be not finite to one: indeed, the set of all $D^2$-bundles over $S^2$ (i.e. every bundle $\csi_c$ with Euler class $c$ and boundary L(c,1), $c \in Z-\{0,-1,-1}$, together with the trivial bundle $S^2 X D^2$) constitutes an infinite family of PL 4-manifolds with the same regular genus (equal to three). Further, general results are obtained, concerning PL 4-manifolds with “restricted gap” between their regular genus and the rank of their fundamental group, especially in case of free fundamental group.
1996
10
279
303
An infinite class of bounded 4-manifolds having regular genus three / Casali, Maria Rita. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. A. - ISSN 0392-4033. - STAMPA. - 10:(1996), pp. 279-303.
Casali, Maria Rita
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/306621
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