Hostname: page-component-84b7d79bbc-lrf7s Total loading time: 0 Render date: 2024-07-26T19:28:02.666Z Has data issue: false hasContentIssue false
  • English
  • Français

Counterexamples to a conjecture about spherical diagrams

Published online by Cambridge University Press:  24 October 2008

S. M. Gersten  and
James Howie
S. M. Gersten
Affiliation:
University of Utah, Salt Lake City, UT 84112, U.S.A.
James Howie
Affiliation:
University of Glasgow, Glasgow G12 8QW
Get access Rights & Permissions [Opens in a new window]

Extract

A spherical diagram over a 2-complex X consists of a tessellation T of the 2-sphere, together with a combinatorial map (that is, one which maps each cell homeomorphically on to a cell). In [2] and [6] a number of conjectures were made concerning spherical diagrams over a 2-complex X with H2(X) = 0. There are also related conjectures in [7]. The motivation for all of these conjectures is that they imply the Kervaire Conjecture: every non-singular system of equations over a group can be solved in some overgroup (see [1, 2, 4, 6, 7] for details and discussion).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 3 , November 1986 , pp. 539 - 543
Copyright
Copyright © Cambridge Philosophical Society 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Gersten, S. M.. Conservative groups, indicability, and a conjecture of Howie. J. Pure Appl. Algebra 29 (1983), 59–74.CrossRefGoogle Scholar
[2]Gersten, S. M.. Nonsingular equations of small weight over groups. Combinatorial Group Theory and Topology, Ann. of Math. Stud. 111 (in the Press).Google Scholar
[3]Gersten, S. M.. Products of conjugacy classes in a free group: a counterexaple. Math. Z. 192 (1986), 167–182.CrossRefGoogle Scholar
[4]Howie, J.. On pairs of 2-complexes and systems of equations over groups. J. Reine Angew. Math. 324 (1981), 165–174.Google Scholar
[5]Howie, J.. The solution of length three equations over groups. Proc. Edinburgh Math. Soc. (2), 26 (1983), 89–96.CrossRefGoogle Scholar
[6]Howie, J.. Spherical diagrams and equations over groups. Math. Proc. Cambridge Philos. Soc. 96 (1984), 255–268.CrossRefGoogle Scholar
[7]Stallings, J. R.. Surfaces in three-manifolds and nonsingular equations in groups. Math. Z. 184 (1983), 1–17.CrossRefGoogle Scholar