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aequationes mathematicae

, Volume 65, Issue 1–2, pp 40–60 | Cite as

On spines of Seifert fibered manifolds

  • B. Ruini
  • F. Spaggiari
  • A. Vesnin
Original paper

Summary.

We define a family of balanced presentations of groups and prove that they correspond to spines of some Seifert fibered 3-manifolds. These presentations of groups (and manifolds) generalize in a natural way many classes of presentations of groups (and manifolds) previously studied by several authors. Moreover, we construct crystallizations representing the small Seifert manifolds of the considered class.

Mathematics Subject Classification (2000). 57M05, 57M20, 57M50, 20F05.¶Keywords. Spine complex, Seifert manifolds, crystallization, fundamental group, groups with balanced presentation. 

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Copyright information

© Birkhäuser Verlag, Basel, 2003

Authors and Affiliations

  • B. Ruini
    • 1
  • F. Spaggiari
    • 2
  • A. Vesnin
    • 3
  1. 1.Dipartimento di Matematica, Università degli Studi di Modena e Reggio Emilia, Via Campi 213/B, I-41100 Modena, Italy, e-mail: ruini@unimo.it IT
  2. 2.Dipartimento di Matematica, Università degli Studi di Modena e Reggio Emilia, Via Campi 213/B, I-41100 Modena, Italy, e-mail: spaggiari@unimo.it IT
  3. 3.Sobolev Institute of Mathematics, pr. Koptyuga 4, Novosibirsk 630090, Russia, e-mail: vesnin@math.nsc.ru RU

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