Glasnik Matematicki, Vol. 40, No.1 (2005), 149-175.
PUPPE EXACT SEQUENCE AND ITS APPLICATION
IN THE FIBREWISE CATEGORY MAP
Yoshifumi Konami and Takuo Miwa
Izumo-Nishi High School, Izumo City 693-0032, Japan
Department of Mathematics, Shimane University,
Matsue 690-8504, Japan
Abstract. In this paper, we study Puppe exact sequence
and its application in the fibrewise category
MAP. The application shows that we can prove the generalized
formula for the suspension of fibrewise product spaces. Further,
introducing an intermediate fibrewise category
we give an another proof of the original
formula in TOPB
using the concepts of
2000 Mathematics Subject Classification.
55R70, 55P05, 55R65.
Key words and phrases. Fibrewise topology, category
MAP, fibrewise pointed homotopy, fibrewise pointed cofibration,
Puppe exact sequence.
Full text (PDF) (free access)
- D. Buhagiar,
The category MAP,
Mem. Fac. Sci. & Eng., Shimane Univ. 34 (2001), 1-19.
- M. Crabb and I. M. James,
Fibrewise homotopy theory, Springer Monographs in Mathematics, 1998.
- R. Engelking,
General topology, Heldermann, Berlin, rev. ed., 1989.
- T. Hotta and T. Miwa,
A new approach to fibrewise fibrations and cofibrations,
Topology and its Appl. 122 (2002), 205-222.
- I. M. James,
Fibrewise topology, Cambridge Univ. Press, Cambridge, 1989.
- T. Miwa,
On fibrewise retraction and extension,
Houston J. Math. 26 (2000), 811-831.
- B. A. Pasynkov,
On extensions to mappings of certain notions and assertions concerning spaces,
Mappings and Functions (Moscow), Izdat. MGU, Moscow, 1984, 72-102 (in Russian).
- B. A. Pasynkov,
Elements of the general topology of continuous maps, On Compactness and
Completeness Properties of Topological Spaces, FAN Acad. of Science of the Uzbek. Rep.,
Tashkent, 1994, 50-120 (in Russian).
- D. Puppe,
Homotopiemengen und ihre induzierten Abbildungen, I,
Math. Z. 69 (1958), 299-344.
- E. H. Spanier,
Algebraic topology, McGraw-Hill, 1966.
Glasnik Matematicki Home Page