A topologist's interactions with Derek J. S. Robinson and his mathematics

Document Type : Dedicated to Prof. D. J. S. Robinson

Author

Department of Mathematics, Bradley University Peoria, IL 61625, U.S.A.

Abstract

The paper begins with a brief history of this topologist's interactions with Derek J. S. Robinson. It continues with a topological proof of Derek's result showing that the Schur multiplier of a generalized Baumslag-Solitar group $G$ is free abelian of rank one less than the rank of the torsion free first homology of $G$ and that both of these ranks can be computed by inspecting a weighted directed graph associate to $G$. In this paper the topology of a special subclass of Seifert fibred 2-dimensional complexes is used to provide proofs of Derek's results.

Keywords

Main Subjects

References

Bedenikovic, A. Delgado, M. Timm, A classification of 2-complexes with nontrivial self-covers, Topology Appl. 153 (2006), no. 12, 2073--2091.
Delgado, D. J. S. Robinson and M. Timm, Generalized Baumslag-Solitar groups and geometric homomorphisms, J. Pure and Appl. Algebra 215 (2011), no. 4, 398--410.
Delgado, D. J. S. Robinson and M. Timm, Generalized Baumslag-Solitar graphs with soluble fundamental groups, Algebra Colloq. 21 (2014), no. 1, 53--58.
Delgado, D. J. S. Robinson and M. Timm, Cyclic normal subgroups of generalized Baumslag-Solitar groups, Comm. Algebra 45 (2017), no. 4, 1808--1818.
Delgado, D. J. S. Robinson and M. Timm, 3 manifolds and generalized Baumslag-Solitar groups, Comm. Anal.Geom. 26 (2018), no. 3, 571--584.
H. Heil, Some finitely presented non-3-manifold groups, Proc. Amer. Math. Soc. 53 (1975), no. 2, 497--500.
Hempel, 3-Manifolds, Ann. of Math. Studies, 86, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976.
Levitt, On the automorphism group of generalized Baumslag-Solitar groups, Geom. Topol. 11 (2007) 473—515, S. Mac Lane, Homology, Springer-Verlag, 1963.
J. S. Robinson, A Course in the Theory of Groups, 1st ed., Springer-Verlag, New York, 1982.
J. S. Robinson, The Schur multiplier of a generalized Baumslag-Solitar group, Rend. Se. Mat. Univ. Padova, 125 (2011) 207--215.
J. S. Robinson, Generalized Baumslag-Solitar groups: a survey of recent progress. Groups St Andrews 2013, 457--468, London Math. Soc. Lecture Note Ser., 422, Cambridge Univ. Press, Cambridge, 2015.
J. S. Robinson, M. Timm, On groups that are isomorphic with every subgroup of finite index and their topology, J. London Math. Society (2) 57 (1998), no. 1, 91--104.
P. Serre, Trees, Translated from the French original by John Stillwell, Corrected 2nd printing of the 1980 English translation, Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2003.
Timm, Generalized Baumslag-Solitar groups: a topological approach, to appear in Groups St Andrews 2022 in Newcastle, London Mathematical Society Lecture Note Serie, Cambridge University Press, Cambridge.
Journal of the Iranian Mathematical Society
Volume 3, Issue 2
July 2022
Pages 75-90

Files

Share

How to cite

Statistics