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S-Maximal Subgroups of πl(M3)

Published online by Cambridge University Press:  20 November 2018

C. D. Feustel
C. D. Feustel*
Affiliation:
Institute for Defense Analyses, Princeton, New Jersey; Virginia Polytechnic and State University, Blacksburg, Virginia
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Let M be a compact, connected, irreducible 3-manifold. Let S be a closed, connected, 2-manifold other than the 2-sphere or projective plane. Let f be a map of S into M such that

Suppose for every closed, connected surface S1 and every map g:S1 → M such that

(1) is an injection,

(1)

Then we shall say that the subgroup is a surface maximal or S-maximal subgroup of π1(M). We may also say that the map f is S-maximal.

Let M be an irreducible 3-manifold which does not admit any embedding of the projective plane. Then we shall say that M is p2-irreducible. Throughout this paper all spaces will be simplicial complexes and all maps will be piecewise linear.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 3 , June 1972 , pp. 439 - 449
Copyright
Copyright © Canadian Mathematical Society 1972

References

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