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Solvable Systems of Equations Modeled on Some Spines of 3-Manifolds

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Abstract

We show solvability of the systems of equations modeled on certain spines of 3-manifolds. We extend a result by Duncan and Howie about the 2-skeleton of the 3-torus.

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References

  1. Howie J., “On pairs of 2-complexes and systems of equations over groups,” J. Reine. Angew. Math., 324, 165–174 (1981).

    Google Scholar 

  2. Gerstenhaber M. and Rothaus O. S., “The solutions of sets of equations in groups,” Proc. Nat. Acad. Sci. U.S.A., 48, 1531–1533 (1962).

    Google Scholar 

  3. Rothaus O. S., “On the non-triviality of some group extensions given by generators and relations,” Ann. of Math., 106, No. 2, 599–612 (1977).

    Google Scholar 

  4. Clifford A., “A class of exponent-sum two equations over groups,” Glasgow Math. J., 44, No. 2, 201–207 (2002).

    Google Scholar 

  5. Edjvet M. and Howie J., “The solution of length four equations over groups,” Trans. Amer. Math. Soc., 326, No. 1, 345–369 (1991).

    Google Scholar 

  6. Gersten S. M., “Nonsingular equations of small weight over groups,” in: Combinatorial Group Theory and Topology (Alta, Utah, 1984), Ann. of Math. Stud., Princeton Univ. Press, 1987, 111, pp. 121–144.

  7. Howie J., “Nonsingular systems of two length three equations over a group,” Math. Proc. Cambridge Philos. Soc., 110, No. 1, 11–24 (1991).

    Google Scholar 

  8. Lyndon R. C., “Equations in groups,” Bull. Amer. Math. Soc., 68, 603–604 (1962).

    Google Scholar 

  9. Ferlini V., Goldstein R., and Salpukas M., “On the solution of certain equations with exponent sum 0 over Z2,” Internat. J. Algebra Comput., 10, No. 6, 709–723 (2000).

    Google Scholar 

  10. Edjvet M., “A singular equation of length four over groups,” Algebra Colloq., 7, No. 3, 247–274 (2000).

    Google Scholar 

  11. Duncan A. J. and Howie J., “The 3-torus is Kervaire,” Contemp. Math., 164, 1–8 (1994).

    Google Scholar 

  12. Howie J., “The solution of length three equations over groups,” Proc. Edinburgh Math. Soc., 26, No. 1, 89–9 (1983).

    Google Scholar 

  13. Lyndon R. and Schupp P., Combinatorial Group Theory, Springer-Verlag, Berlin, Heidelberg, and New York (1977).

    Google Scholar 

Download references

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Authors and Affiliations

  1. Heriot-Watt University, Edinburgh

    N. V. Kopteva

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  1. N. V. Kopteva
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Kopteva, N.V. Solvable Systems of Equations Modeled on Some Spines of 3-Manifolds. Siberian Mathematical Journal 44, 278–285 (2003). https://doi.org/10.1023/A:1022984804581

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