Open Access
April, 2009 Composition properties of box brackets
Howard J. MARCUM, Nobuyuki ODA
J. Math. Soc. Japan 61(2): 507-549 (April, 2009). DOI: 10.2969/jmsj/06120507


In the homotopy theory of a 2-category with zeros and having a suspension functor we establish various composition properties of box brackets, including new formulae involving 2-sided matrix Toda brackets and classical Toda brackets. We are lead to define and study a new secondary homotopy operation called the box quartet operation. In the topological category this operation satisfies two triviality properties, one of which may be viewed as the foundation upon which an important classical mod zero result on Toda brackets rests. New insights and computations in the homotopy groups of spheres are obtained.


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Howard J. MARCUM. Nobuyuki ODA. "Composition properties of box brackets." J. Math. Soc. Japan 61 (2) 507 - 549, April, 2009.


Published: April, 2009
First available in Project Euclid: 13 May 2009

zbMATH: 1226.18005
MathSciNet: MR2532899
Digital Object Identifier: 10.2969/jmsj/06120507

Primary: 18D05 , 55P40 , 55Q35 , 55Q40

Keywords: 2-category , box bracket , box quartet operation , homotopy groups of spheres , suspension functor , Toda bracket

Rights: Copyright © 2009 Mathematical Society of Japan

Vol.61 • No. 2 • April, 2009
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