Homogeneous inverse limit spaces with nonregular covering maps as bonding maps

Authors:
James T. Rogers and Jeffrey L. Tollefson

Journal:
Proc. Amer. Math. Soc. **29** (1971), 417-420

MSC:
Primary 54.25

DOI:
https://doi.org/10.1090/S0002-9939-1971-0273561-5

MathSciNet review:
0273561

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Abstract | References | Similar Articles | Additional Information

Abstract: We construct counterexamples to the conjecture that, in an inverse sequence of closed manifolds with covering maps as bonding maps, if the inverse limit space is homogeneous, then there exists an integer *m* such that (for all ) the covering map is regular.

**[1]**S. Eilenberg and N. Steenrod,*Foundations of algebraic topology*, Princeton Univ. Press, Princeton, N. J., 1952. MR**14**, 398. MR**0050886 (14:398b)****[2]**M. C. McCord,*Inverse limit sequences with covering maps as bonding maps*, Trans. Amer. Math. Soc.**114**(1965), 197-209. MR**30**#3450. MR**0173237 (30:3450)****[3]**J. T. Rogers, Jr. and J. L. Tollefson,*Involutions on solenoidal spaces*, Fund. Math. (to appear). MR**0296923 (45:5982)****[4]**E. H. Spanier,*Algebraic topology*, McGraw-Hill, New York, 1966. MR**35**#1007. MR**0210112 (35:1007)****[5]**R. M. Schori,*Inverse limits and homogeneity*, Trans. Amer. Math. Soc.**124**(1966), 533-539. MR**33**#6574. MR**0198416 (33:6574)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0273561-5

Keywords:
Inverse limits,
weak solenoidal spaces,
normal series,
covering map,
homogeneity

Article copyright:
© Copyright 1971
American Mathematical Society