Given two closed oriented n-manifolds M and N, M is said to dominate N if a non-zero degree map from M to N exists. From dimension n = 3 on, the domination relation fails to be an ordering. By a result of [Math. Semin. Notes, Kobe Univ. 9, 159-180 (1981; Zbl 0483.57003)], every 3-manifold turns out to be dominated by a surface bundle over the circle; on the other hand, in [J. Lond. Math. Soc. 79 (3), 545-561 (2009; Zbl 1168.53024)] and [Groups Geom. Dyn. 7 (1), 181-204 (2013; Zbl 06147449)] it is shown that 3-manifolds dominated by products cannot have hyperbolic or Sol3-geometry, and must often be prime. In the present paper, the authors give a complete characterization of 3-manifolds dominated by products, by proving that a closed oriented 3-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of S2 × S1. It is worthwhile to note that the same characterization may also be formulated in terms of Thurston geometries, or in terms of purely algebraic properties of the fundamental group. Moreover, the authors determine which 3-manifolds are dominated by non-trivial circle bundles, and which 3-manifold groups are presentable by products (according to [J. Lond. Math. Soc. 79 (3), 545-561 (2009; Zbl 1168.53024)]).

REVIEW OF: "Kotschick D. - Neofytidis, C., On three-manifolds dominated by circle bundles, Math. Z. 274, No. 1-2, 21-32 (2013)". [DE06176500X] / Casali, Maria Rita. - In: EXCERPTS FROM ZENTRALBLATT MATH. - ISSN 2190-3484. - ELETTRONICO. - Zbl 1277.57003:(2013), pp. .-...

REVIEW OF: "Kotschick D. - Neofytidis, C., On three-manifolds dominated by circle bundles, Math. Z. 274, No. 1-2, 21-32 (2013)". [DE06176500X]

CASALI, Maria Rita
2013

Abstract

Given two closed oriented n-manifolds M and N, M is said to dominate N if a non-zero degree map from M to N exists. From dimension n = 3 on, the domination relation fails to be an ordering. By a result of [Math. Semin. Notes, Kobe Univ. 9, 159-180 (1981; Zbl 0483.57003)], every 3-manifold turns out to be dominated by a surface bundle over the circle; on the other hand, in [J. Lond. Math. Soc. 79 (3), 545-561 (2009; Zbl 1168.53024)] and [Groups Geom. Dyn. 7 (1), 181-204 (2013; Zbl 06147449)] it is shown that 3-manifolds dominated by products cannot have hyperbolic or Sol3-geometry, and must often be prime. In the present paper, the authors give a complete characterization of 3-manifolds dominated by products, by proving that a closed oriented 3-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of S2 × S1. It is worthwhile to note that the same characterization may also be formulated in terms of Thurston geometries, or in terms of purely algebraic properties of the fundamental group. Moreover, the authors determine which 3-manifolds are dominated by non-trivial circle bundles, and which 3-manifold groups are presentable by products (according to [J. Lond. Math. Soc. 79 (3), 545-561 (2009; Zbl 1168.53024)]).
.
..
Casali, Maria Rita
REVIEW OF: "Kotschick D. - Neofytidis, C., On three-manifolds dominated by circle bundles, Math. Z. 274, No. 1-2, 21-32 (2013)". [DE06176500X] / Casali, Maria Rita. - In: EXCERPTS FROM ZENTRALBLATT MATH. - ISSN 2190-3484. - ELETTRONICO. - Zbl 1277.57003:(2013), pp. .-...
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/11380/1061910
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact