Universal presentations for manifold groups

We construct a universal presentation for the fundamental group of a closed-connected orientable 3-manifold. This result may be of considerable interest not only for topologists but also for experts in combinatorial group theory. Some applications on periodic manifolds and geometric presentations complete the paper.

[1]  W. B. R. Lickorish,et al.  A Representation of Orientable Combinatorial 3-Manifolds , 1962 .

[2]  A. Vesnin,et al.  Fractional Fibronacci groups and manifolds , 1998 .

[3]  Moto-O. Takahashi On the presentations of the fundamental groups of 3-manifolds , 1989 .

[4]  A. Cavicchioli,et al.  Surgery on 3-manifolds with S-1-actions , 1996 .

[5]  D. L. Johnson,et al.  Topics in the Theory of Group Presentations: Frontmatter , 1980 .

[6]  H. Hilden,et al.  The arithmeticity of the figure eight knot orbifolds , 1992 .

[7]  Dušan D. Repovš,et al.  Families of group presentations related to topology , 2005 .

[8]  Robion Kirby,et al.  A calculus for framed links inS3 , 1978 .

[9]  W. Lickorish A Foliation for 3-Manifolds , 1965 .

[10]  W. Thurston The geometry and topology of 3-manifolds , 1979 .

[11]  Eugénia César de Sá A link calculus for 4-manifolds , 1979 .

[12]  J. Przytycki,et al.  Surgeries on periodic links and homology of periodic 3-manifolds , 2000, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  H. Hilden,et al.  On universal groups and three-manifolds , 1987 .

[14]  A. Cavicchioli,et al.  Surgery on 3-manifolds with $$\mathbb{S}$$ 1-actions , 1996 .

[15]  C. Rourke,et al.  On Kirby's calculus of links , 1979 .

[16]  R. S. Stevens,et al.  Group presentations corresponding to spines of 3-manifolds. III , 1977 .

[17]  J. Montesinos SURGERY ON LINKS AND DOUBLE BRANCHED COVERS OF S3 , 1975 .

[18]  D. Rolfsen Knots and Links , 2003 .

[19]  A. Wallace Modifications and Cobounding Manifolds , 1960, Canadian Journal of Mathematics.

[20]  Dušan D. Repovš,et al.  TOPOLOGICAL PROPERTIES OF CYCLICALLY PRESENTED GROUPS , 2003 .

[21]  M. Mulazzani On periodic Takahashi manifolds , 2001, math/0104224.

[22]  R. S. Stevens,et al.  Group Presentations Corresponding to Spines of 3-Manifolds 1 , 1974 .

[23]  B. Ruini,et al.  On the structure of Takahashi manifolds , 1998 .