In this work, (orientable and non-orientable) 4-dimensional handlebodies are proved to be the only 4-manifolds whose regular genus equals the one of their boundary. As a consequence, we obtain the classification of all 4-manifolds of regular genus g less-than-or-equal-to 1.
A combinatorial characterization of 4-dimensional handlebodies / Casali, Maria Rita. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - STAMPA. - 4:(1992), pp. 123-134. [10.1515/form.1992.4.123]
A combinatorial characterization of 4-dimensional handlebodies
CASALI, Maria Rita
1992
Abstract
In this work, (orientable and non-orientable) 4-dimensional handlebodies are proved to be the only 4-manifolds whose regular genus equals the one of their boundary. As a consequence, we obtain the classification of all 4-manifolds of regular genus g less-than-or-equal-to 1.
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