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Geometric realizations for free quotients

Published online by Cambridge University Press:  09 April 2009

William Jaco
William Jaco
Affiliation:
Department of MathematicsRice UniversityHouston, Texas U.S.A.
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In [7] Lyndon introduced the concept of inner rank for groups. He defined the inner rank of an arbitrary group G to be the upper bound of the ranks of free homomorphic images of G. Both Lyndon and Jaco have shown that the inner rank of the fundamental group of a closed 2-manifold with Euler characteristic 2 − p, p ≧ 0, is [p/2] where [p/2] is the greatest integer ≦ p/2. The proof given by lyndon [8] uses algebraic techniques; whereas, the proof by Jaco [4] is geometrical.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 4 , December 1972 , pp. 411 - 418
Copyright
Copyright © Australian Mathematical Society 1972

References

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