Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T09:05:29.066Z Has data issue: false hasContentIssue false
  • English
  • Français

Colour Switching and Homeomorphism of Manifolds

Published online by Cambridge University Press:  20 November 2018

Massimo Ferri
Massimo Ferri*
Affiliation:
Universita di Bologna, Bologna, Italia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Throughout this paper, we work in the PL and pseudosimplicial categories, for which we refer to [17] and [10] respectively. For the graph theory involved see [9].

An h-coloured graph (Γ, γ) is a multigraph Γ = (V(Γ), E(Γ)) regular of degree h, endowed with an edge-coloration γ by h colours. If is the colour set, for each we set

For each set . For n ∊ Z, n ≧ 1, set

Δn will be mostly used to denote the colour set for an (n + 1)-coloured graph.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 1 , 01 February 1987 , pp. 8 - 32
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Ferri, M., Una rappresentazione délie n-vahetà topologiche triangolabili mediante grafi (n, + 1)-colorati, Boll. Un. Mat. Ital. 13B (1976), 250–260.Google Scholar
2. Ferri, M., Crystallisations of 2-fold branched coverings of S3 , Proc. Amer. Math. Soc. 73 (1979), 271–276.Google Scholar
3. Ferri, M. and Gagliardi, C., Crystallisation moves, Pacific J. Math. 100 (1982), 85–103.Google Scholar
4. Ferri, M. and Gagliardi, C., The only genus zero n-manifold is Sn , Proc. Amer. Math. Soc. 85 (1982), 638–642.Google Scholar
5. Ferri, M. and Gagliardi, C., On the genus of 4-dimensional products of manifolds, Geom. Dedicata 13 (1982), 331–345.Google Scholar
6. Ferri, M., Gagliardi, C. and Grasselli, L., A graph-theoretical representation of PL-manifolds — A survey on crystallizations, Aequationes Math. 31 (1986), 121–141.Google Scholar
7. Gagliardi, C., Regular imbeddings of edge-coloured graphs, Geom. Dedicata 11 (1981), 397–414.Google Scholar
8. Gagliardi, C., Extending the concept of genus to dimension n, Proc. Amer. Math. Soc. 81 (1981), 473–481.Google Scholar
9. Harary, F., Graph theory, (Addison Wesley, 1968).Google Scholar
10. Hilton, P. J. and Wylie, S., An introduction to algebraic topology — Homology theory, (Cambridge University Press, 1960).CrossRefGoogle Scholar
11. Kirby, R., Problems in low-dimensional manifold theory, Proc. Symp. Pure Math. 32 (1978), 273–312.Google Scholar
12. Lins, S., Graphs of maps, Ph. D. Thesis, University of Waterloo (1980).Google Scholar
13. Lins, S., Graph-encoded maps, J. Combin. Theory Ser. B 32 (1982), 171–181.Google Scholar
14. Lins, S. and Mandel, A., Graph-encoded 3-manifolds, Discrete Math. 57 (1985), 261–284.Google Scholar
15. Pezzana, M., Sulla struttura topologica délie varietà compatte, Atti Sem. Mat. Fis. Univ. Modena 23 (1974), 278–285.Google Scholar
16. Pezzana, M., Diagrammi di Heegaard e triangolazione contratta, Boll. Un. Mat. Ital. 12, Suppl. fasc. 3 (1975), 98–105.Google Scholar
17. Rourke, C. and Sanderson, B., Introduction to piecewise-linear topology, (Springer Verlag, 1972).CrossRefGoogle Scholar
18. Vince, A., Graphic matroids, shellability and the Poincaré conjecture, Geom. Dedicata 14 (1983), 303–314.Google Scholar