Constructing -maps between spheres

Author:
Steven C. Ferry

Journal:
Proc. Amer. Math. Soc. **120** (1994), 329-332

MSC:
Primary 57Q99; Secondary 57N60

DOI:
https://doi.org/10.1090/S0002-9939-1994-1166355-5

MathSciNet review:
1166355

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Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this note is to give a quick proof of an extremely counterintuitive theorem of Bestvina, Walsh, and Wilson. The theorem says, for example, that the degree map is homotopic to a map such that is connected for each .

**[1]**R. D. Anderson,*Open mappings of compact continua*, Proc. Nat. Acad. Sci. U.S.A.**42**(1956), 347-349. MR**0078682 (17:1230h)****[2]**M. Bestvina,*Characterizing*-*dimensional universal Menger compacta*, Mem. Amer. Math. Soc., no. 71, Amer. Math. Soc., Providence, RI, 1988. MR**920964 (89g:54083)****[3]**A. V. Černavskii,*A generalization of Keldysh's construction of a monotone map of a cube onto a cube of higher dimension*, Russian Math. Surveys**40**(1985), 165-167.**[4]**M. M. Cohen,*A course in simple-homotopy theory*, Springer-Verlag, New York, 1970. MR**0362320 (50:14762)****[5]**S. C. Ferry,*A stable converse to the Vietoris-Smale theorem with applications to shape theory*, Trans. Amer. Math. Soc.**261**(1980), 369-386. MR**580894 (82c:55018)****[6]**-,*Mapping manifolds to polyhedra*, preprint.**[7]**L. V. Keldýs,*A monotone map of a cube onto a cube of higher dimension*, Mat. Sb.**41**(1957), 129-158. MR**0090805 (19:874g)****[8]**R. C. Lacher,*Cell-like mappings and their generalizations*, Bull. Amer. Math. Soc.**83**(1977), 495-552. MR**0645403 (58:31095)****[9]**J. J. Walsh,*A general method of constructing*-*mappings on manifolds with applications to spheres*, preprint, 1974.**[10]**J. H. C. Whitehead,*Simplicial spaces, nucleii, and*-*groups*, Proc. London Math. Soc. (3)**45**(1939), 243-327.**[11]**D. Wilson,*On constructing monotone and**mappings of arbitrary degree*, Duke Math. J.**40**(1973), 103-109. MR**0339250 (49:4011)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1166355-5

Keywords:
Space-filling curve,
-map,
cell-like map

Article copyright:
© Copyright 1994
American Mathematical Society