Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Coincidence point results for spaces with free $ Z\sb{p}$-actions


Authors: Fred Cohen and Ewing L. Lusk
Journal: Proc. Amer. Math. Soc. 49 (1975), 245-252
MSC: Primary 55C20
DOI: https://doi.org/10.1090/S0002-9939-1975-0372846-5
MathSciNet review: 0372846
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ support a free cyclic group action of prime order. We consider the question of determining when any map $ f:X \to Y$ must identify two points of an orbit, and that of finding the minimum possible dimension of the union of such orbits when they exist.


References [Enhancements On Off] (What's this?)

  • [1] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 17, 1040. MR 0077480 (17:1040e)
  • [2] T. Chang and T. Skjelbred, Group actions on Poincaré duality spaces, Bull. Amer. Math. Soc. 78 (1972), 1024-1026. MR 0307226 (46:6346)
  • [3] F. Cohen and J. E. Connett, A coincidence theorem related to the Borsuk-Ulam theorem, Proc. Amer. Math. Soc. 44 (1974), 218-220. MR 0331374 (48:9707)
  • [4] J. E. Connett, A generalization of the Borsuk-Ulam theorem, J. London Math. Soc. (2) 7 (1973), 64-66. MR 0322856 (48:1217)
  • [5] P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Band 33, Academic Press, New York; Springer-Verlag, Berlin, 1964. MR 31 #750. MR 0176478 (31:750)
  • [6] E. Fadell and L. Neuwirth, Configuration spaces, Math. Scand. 10 (1962), 111-118. MR 25 #4537. MR 0141126 (25:4537)
  • [7] D. L. Johnson, On the cohomology of finite $ 2$-groups, Invent. Math. 7 (1969), 159-173. MR 39 #6986. MR 0245680 (39:6986)
  • [8] S. Mac Lane, Homology, Springer-Verlag, New York, 1967. MR 1344215 (96d:18001)
  • [9] H. J. Munkholm, Borsuk-Ulam type theorems for proper $ {{\mathbf{Z}}_p}$-actions on ($ \bmod p$ homology) $ n$-spheres, Math. Scand. 24 (1969), 167-185 (1970). MR 41 #2672. MR 0258025 (41:2672)
  • [10] T. Skjelbred, A lemma on the spectral sequence of the action of a finite group with periodicity (unpublished).
  • [11] R. G. Swan, The $ p$-period of a finite group, Illinois J. Math. 4 (1960), 341-346. MR 23 #A188. MR 0122856 (23:A188)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55C20

Retrieve articles in all journals with MSC: 55C20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0372846-5
Keywords: Coincidence points, cyclic group actions, configuration spaces
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society