Volume 10 (2007)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Other MSP Publications

Determination of the multiplicative nilpotency of self-homotopy sets

Ken-ichi Maruyama

Geometry & Topology Monographs 10 (2007) 281–292

DOI: 10.2140/gtm.2007.10.281

arXiv: 0903.4607

Abstract

The semigroup of the homotopy classes of the self-homotopy maps of a finite complex which induce the trivial homomorphism on homotopy groups is nilpotent. We determine the nilpotency of these semigroups of compact Lie groups and finite Hopf spaces of rank 2. We also study the nilpotency of semigroups for Lie groups of higher rank. Especially, we give Lie groups with the nilpotency of the semigroups arbitrarily large.

Keywords

self-homotopy sets, Lie groups, H–spaces

Mathematical Subject Classification

Primary: 55P10, 55Q05, 57T20

Secondary: 20D15, 55P60

References
Publication

Received: 13 August 2004
Revised: 22 June 2005
Published: 29 January 2007

Authors
Ken-ichi Maruyama
Faculty of Education
Chiba University
Chiba 263-8522
Japan