#### 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

*e-mail:* `miwa@riko.shimane-u.ac.jp`

**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
**TOP**^{H}_{B},
we give an another proof of the original
formula in **TOP**_{B}
using the concepts of
**TOP**^{H}_{B}.

**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)
DOI: 10.3336/gm.40.1.14

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CrossRef

- E. H. Spanier,
Algebraic topology, McGraw-Hill, 1966.

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