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One-Dimensional Cell Complexes with Homeotopy Group Equal to Zero

Published online by Cambridge University Press:  20 November 2018

Louis V. Quintas
Louis V. Quintas*
Affiliation:
City College, New York and St. John's University, New York
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Let K denote a connected finite 1-dimensional cell complex (1, p. 95), G(K) its group of homeomorphisms, and D(K) the group of homeomorphisms of K which are isotopic to the identity. The group (K) = G(K)/D(K) is a topological invariant of K and is called the homeotopy group ofK (4). K may be thought of as a linear graph (connected finite 1- dimensional simplicial complex) extended to admit loops and multiple edges and (K) as the topological analogue of the automorphism group A(L), (the permutations of vertices which preserve edge incidence relations) of a linear graph L.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 353 - 357
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Hilton, P. J., An introduction to homotopy theory (Cambridge, 1953).Google Scholar
2. Kagno, I. N., Desargues1 and Pappus’ graphs and their groups, Am. J. Math., 69 (1947).Google Scholar
3. Kagno, I. N., Linear graphs of degree ≤ 6 and their groups, Am. J. Math., 68 (1946), 505–520. For corrections, see Am. J. Math., 69 (1947), 872 and Am. J. Math., 77 (1955), 392.Google Scholar
4. McCarty, G. S. Jr., Homeotopy groups, Trans. Am. Math. Soc, 106 (1963), 293–304.Google Scholar