Comultiplications on a wedge of two spheres  

作　　者：ARKOWITZ Martin LEE Dae-Woong 

机构地区：[1]Department of Mathematics,Dartmouth College [2]Department of Mathematics and Institute of Pure and Applied Mathematics,Chonbuk National University

出　　处：《Science China Mathematics》2011年第1期9-22,共14页中国科学：数学（英文版）

摘　　要：In this paper we study the set of comultiplications on a wedge of two spheres. We are primarily interested in the size of this set and properties of the comultiplications such as associativity and commutativity. Our methods involve Whitehead products in wedges of spheres and the Hopf-Hilton invariants. We apply our results to specific examples and determine the number of comultiplications, associative comultiplications and commutative comultiplications in these cases.In this paper we study the set of comultiplications on a wedge of two spheres. We are primarily interested in the size of this set and properties of the comultiplications such as associativity and commutativity. Our methods involve Whitehead products in wedges of spheres and the Hopf-Hilton invariants. We apply our results to specific examples and determine the number of comultiplications, associative comultiplications and commutative comultiplications in these cases.

关 键 词：co-H-spaces comultiplications homotopy associativity homotopy commutativity basic Whitehead products Hilton’s formula Hopf-Hilton invariants 

分 类 号：O177[理学—数学]