Abstract
In this paper we study the set of comultiplications on a wedge of a finite number of spheres. We are interested in group theoretic properties of these comultiplications such as associativity and commutativity and loop theoretic properties such as inversivity, power-associativity and the Moufang property. Our methods involve Whitehead products in wedges of spheres and the Hopf-Hilton invariants. We obtain extensive results for a restricted class of comultiplications, namely, the one-stage quadratic or cubic comultiplications.
| Original language | English |
|---|---|
| Pages (from-to) | 1607-1621 |
| Number of pages | 15 |
| Journal | Topology and its Applications |
| Volume | 157 |
| Issue number | 9 |
| DOIs | |
| State | Published - 2010.06 |
Keywords
- Algebraic loops
- Co-H-spaces
- Comultiplications
- Homotopy associativity
- Homotopy commutativity
- Hopf-Hilton invariants
- Inversivity
- Power-associativity
- Secondary
- The Moufang property
- Wedges of spheres
- Whitehead products
Quacquarelli Symonds(QS) Subject Topics
- Mathematics
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