Two special cases of Ganea's conjecture

Author:
Jeffrey A. Strom

Journal:
Trans. Amer. Math. Soc. **352** (2000), 679-688

MSC (1991):
Primary 55M30, 55P50; Secondary 55P42

DOI:
https://doi.org/10.1090/S0002-9947-99-02046-2

Published electronically:
September 17, 1999

MathSciNet review:
1443893

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Ganea conjectured that for any finite CW complex and any , . In this paper we prove two special cases of this conjecture. The main result is the following. Let be a -connected -dimensional CW complex (not necessarily finite). We show that if and (which implies ), then . This is proved by showing that in a much larger range, and then showing that under the conditions imposed, . The second special case is an extension of Singhof's earlier result for manifolds.

**1.**Blakers and W. Massey: The homotopy groups of a triad, II.*Ann. Math.*(1952) 192-201. MR**13:485f****2.**T. Ganea: Some problems on numerical homotopy invariants.*Lecture Notes in Mathematics*249 (1971) 23-30. MR**49:3910****3.**W. J. Gilbert: Some examples for weak category and conilpotency,*Ill. J. Math.***12**(1968), 421-432. MR**37:6930****4.**K. P. Hess: A proof of Ganea's conjecture for rational spaces.*Topology*,**30**(1991), 205-214. MR**92d:55012****5.**N. Iwase: Ganea's conjecture on Lusternik-Schnirelmann category.*Bull. London Math. Society***30**(1998), 623-634. CMP**98:17****6.**I. M. James: On category in the sense of Lusternik and Schnirelmann.*Topology*,**17**(1978), 331-348. MR**80i:55001****7.**L. Montejano: A quick proof of Singhof's theorem.*Manuscripta Math.*,**42**(1983), 49-52. MR**85a:55002****8.**Y. Rudyak: On category weight and its applications.*Topology*,**38**(1999), 37-55. MR**99f:55007****9.**W. Singhof: Minimal coverings of manifolds with balls.*Manuscripta Math.*,**29**(1979), 385-415. MR**80k:55012****10.**P. A. Schweitzer: Secondary cohomology operations induced by the diagonal mapping.*Topology*.**3**(1965), 337-355. MR**32:451****11.**J. Strom, Category weight and essential category weight, Ph.D thesis, University of Wisconsin (1997).**12.**R. Switzer:*Algebraic Topology: Homotopy and Homology*. Springer-Verlag (1975). MR**52:6695****13.**G. W. Whitehead:*Elements of Homotopy Theory*. Springer-Verlag (1978). MR**80b:55001**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (1991):
55M30,
55P50,
55P42

Retrieve articles in all journals with MSC (1991): 55M30, 55P50, 55P42

Additional Information

**Jeffrey A. Strom**

Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706

Address at time of publication:
Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755

Email:
jeffrey.strom@dartmouth.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02046-2

Received by editor(s):
January 23, 1997

Published electronically:
September 17, 1999

Article copyright:
© Copyright 1999
American Mathematical Society