We determine bounds for the regular genus of any 4-manifold, which is the product of S^1 by a closed 3-manifold, or a product of two closed surfaces. This is done by an explicit construction of a graph representing the manifold, and by finding a minimal regular imbedding of it. Note that the same construction in dimension 3 enables to find the Heegaard genus of S^1 by a closed surbface, thus improving a result obtained, for the orientable case, by M. Ochiai in Yokohama Math J., 25 (1977), 109-112.

On the genus of 4-dimensional products of manifolds / M., Ferri; Gagliardi, Carlo. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - STAMPA. - 13:(1982), pp. 331-345.

On the genus of 4-dimensional products of manifolds

GAGLIARDI, Carlo
1982

Abstract

We determine bounds for the regular genus of any 4-manifold, which is the product of S^1 by a closed 3-manifold, or a product of two closed surfaces. This is done by an explicit construction of a graph representing the manifold, and by finding a minimal regular imbedding of it. Note that the same construction in dimension 3 enables to find the Heegaard genus of S^1 by a closed surbface, thus improving a result obtained, for the orientable case, by M. Ochiai in Yokohama Math J., 25 (1977), 109-112.
13
331
345
On the genus of 4-dimensional products of manifolds / M., Ferri; Gagliardi, Carlo. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - STAMPA. - 13:(1982), pp. 331-345.
M., Ferri; Gagliardi, Carlo
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/584467
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? ND
social impact