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)

 
 

 

Configuration-like spaces and the Borsuk-Ulam theorem


Authors: Fred Cohen and Ewing L. Lusk
Journal: Proc. Amer. Math. Soc. 56 (1976), 313-317
MSC: Primary 55C20
DOI: https://doi.org/10.1090/S0002-9939-1976-0425949-1
MathSciNet review: 0425949
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Some extensions of the classical Borsuk-Ulam Theorem are proved by computing a bound on the homology of certain spaces similar to configuration spaces. The Bourgin-Yang Theorem and a generalization due to Munkholm are special cases of these results.


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

  • [1] K. Borsuk, Drei Sätze über die $ n$-dimensional Euklidische Sphäre, Fund. Math. 20 (1933), 177-190.
  • [2] D. G. Bourgin, On some separation and mapping theorems, Comment. Math. Helv. 29 (1955), 199-214. MR 17, 289. MR 0072469 (17:289d)
  • [3] F. Cohen and J. Connett, A coincidence theorem related to the Borsuk-Ulam theorem, Proc. Amer. Math. Soc. 44 (1974), 218-220. MR 0331374 (48:9707)
  • [4] F. Cohen and E. L. Lusk, Coincidence point results for spaces with free $ {{\mathbf{Z}}_p}$-actions, Proc. Amer. Math. Soc. 49 (1975), 245-252. MR 0372846 (51:9050)
  • [5] E. Fadell and L. Neuwirth, Configuration spaces, Math. Scand. 10 (1962), 111-118. MR 25 #4537. MR 0141126 (25:4537)
  • [6] 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)
  • [7] C.-T. Yang, Continuous functions from spheres to euclidean spaces, Ann. of Math. (2) 62 (1955), 284-292. MR 17, 289. MR 0072471 (17:289f)

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/S0002-9939-1976-0425949-1
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society