On Fox spaces and Jacobi identities

Details On Fox spaces and Jacobi identities On Fox spaces and Jacobi identities

2006-01-16

arxiv.org/abs/math/0601368v2

Math. J. Okayama Univ. 50 (2008), 161--176

Mathematics

Algebraic Topology

16 pages

Scientific paper

In 1945, R. Fox introduced the so-called Fox torus homotopy groups in which the usual homotopy groups are embedded and their Whitehead products are expressed as commutators. A modern treatment of Fox torus homotopy groups and their generalization has been given and studied. In this note, we further explore these groups and their properties. We discuss co-multiplications on Fox spaces and a Jacobi identity for the generalized Whitehead products and the $\Gamma$-Whitehead products.

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