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A proof of the homotopy push-out and pull-back lemma
Author(s):
Michihiro
Sakai
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2461-2466.
MSC (2000):
Primary 55R70
Posted:
January 17, 2001
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Abstract:
The homotopy push-out and pull-back lemma of Iwase (1998) is a generalized version of Theorem 1.1 of Ganea (1965) and the Theorem of Rutter (1971) whose proofs were given under the simply-connectivity condition. The purpose of this paper is to give a proof in the general case.
References:
-
- [1]
- M. C. Crabb and I. M. James, Fibrewise Homotopy Theory, Springer (1998). MR 99k:55001
- [2]
- T. Ganea, A generalization of the homology and homotopy suspension, Comm. Math. Helv. 39 (1965), 295-322. MR 31:4033
- [3]
- N. Iwase, Ganea's conjecture on Lusternik-Schnirelmann category, Bull. London Math. Soc. 30 (1998), 623-634. MR 99j:55003
- [4]
- I. M. James, General topology and Homotopy theory, Springer (1984). MR 86d:55001
- [5]
- I. M. James, Handbook of Algebraic Topology, North-Holland (1995). MR 96g:55002
- [6]
- J. W. Rutter, On a theorem of T. Ganea, J. London Math. Soc. (2) 3 (1971), 190-192. MR 43:5532
- [7]
- M. Sakai, Functors on the category of quasi-fibrations, Kyushu University preprint series in mathematics, 1999-25.
- [8]
- N. E. Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967), 133-152. MR 35:970
- [9]
- G. W. Whitehead, Elements of Homotopy Theory, Springer Verlag, Berlin, GTM series 61 (1978). MR 80b:55001
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Additional Information:
Michihiro
Sakai
Affiliation:
Graduate school of Mathematics, Kyushu University, Fukuoka, Japan, 812-8581
Email:
msakai@math.kyushu-u.ac.jp
DOI:
10.1090/S0002-9939-01-05856-7
PII:
S 0002-9939(01)05856-7
Keywords:
Homotopy push-out,
homotopy pull-back,
NDR-pair
Received by editor(s):
December 1, 1999
Posted:
January 17, 2001
Communicated by:
Ralph Cohen
Copyright of article:
Copyright
2001,
American Mathematical Society
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