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Surface symmetry and homology

Published online by Cambridge University Press:  24 October 2008

Allan L. Edmonds  and
John H. Ewing
Allan L. Edmonds
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405, U.S.A.
John H. Ewing
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405, U.S.A.
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Extract

In his study of the structure of periodic homeomorphisms of surfaces, Jakob Nielsen [7] asked, in effect, how much about an effective group action on a surface is determined by its induced action on homology. (It is well known that the induced action on homology is faithful, provided the surface has negative Euler characteristic. See Farkas and Kra[3], v·3, for example.) Two periodic maps T1 and T2 on an oriented surface M are conjugate if there is an orientation preserving homeomorphism h: M → M such that hT1h–1 = T2; the two maps T1 and T2 are symplectically equivalent if there is an orientation preserving homeomorphism h: M → M so that hT1h–1 and T2 induce the same automorphisms on H1(M). By standard results this is the same as T1* and T2* being conjugate by an automorphism of H1(M) which preserves intersection numbers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 73 - 77
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

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