Norio Iwase
Mailing Adress: Faculty of Mathematics, Kyushu University, Fukuoka 810-8560
E-mail Adress: iwase_AT_math.kyushu-u.ac.jp
Authors.
myself
Journal.
Bull. London Math. Soc. 30 (1998), no. 6, 623-634.
Abstract.
Problem 2 paused by Tudor Ganea is a question on Lusternik-Schnirelmann category, or LS category for short:
Is the LS category of a space increased by 1 by taking the product with a sphere?
The affirmative answer was usually supposed to be true and come to be called as 'Ganea's conjecture' or 'the Ganea conjecture' on LS category.
In this paper, a series of complexes Qp indexed by all primes p is constructed with cat Qp = 2 and cat QpxSn = 2 for either n > 1 or n = 1 and p = 2.
This disproves Ganea's conjecture on LS category.
- Ganea's conjecture on LS-category (adobe-pdf file, 233171 bytes)
- Ganea's conjecture on LS-category (postscript file, 394405 bytes)