#### Algebraic and Geometric Topology 4 (2004),
paper no. 36, pages 829-839.

## Implications of the Ganea Condition

### Norio Iwase, Donald Stanley and Jeffrey Strom

**Abstract**.
Suppose the spaces X and X cross A have the same
Lusternik-Schnirelmann category: cat(X cross A)= cat(X). Then there is
a strict inequality cat(X cross (A halfsmash B)) < cat (X) + cat(A
halfsmash B) for every space B, provided the connectivity of A is
large enough (depending only on X). This is applied to give a partial
verification of a conjecture of Iwase on the category of products of
spaces with spheres.
**Keywords**.
Lusternik-Schnirelmann category, Ganea conjecture, product formula, cone length

**AMS subject classification**.
Primary: 55M30.

**DOI:** 10.2140/agt.2004.4.829

**E-print:** `arXiv:math.AT/0410374`

Submitted: 6 March 2004.
Accepted: 30 September 2004.
Published: 7 October 2004.

Notes on file formats
Norio Iwase, Donald Stanley and Jeffrey Strom

Faculty of Mathematics, Kyushu University, Ropponmatsu
4-2-1

Fukuoka 810-8560, Japan

Department of Mathematics and
Statistics, University of Regina, College West 307.14

Regina,
Saskatchewan, Canada

Department of Mathematics, Western Michigan
University, 1903 W. Michigan Ave

Kalamazoo, MI 49008, USA

Email: iwase@math.kyushu-u.ac.jp, stanley@math.uregina.ca, jeffrey.strom@wmich.edu

AGT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**