Geodesic
σ4-Actions On Homotopy Spheres
Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 275-281

Voir la notice de l'article provenant de la source Cambridge University Press

Let σ4 denote the group of all permutations of {a, b, c, d}. It has 24 elements, partitioned into five conjugacy classes: (1) the identity 1; (2) 6 transpositions: (ab), ..., (cd); (3) 8 elements of order 3: (abc), ..., (bcd); (4) 6 elements of order 4: (abcd), ..., (adcb); (5) 3 elements of order 2: x = (ab)(cd), y = (ac)(bd), z = (ad)(bc).In this paper, we study the differentiate actions of σ4 on odd-dimensional homotopy spheres modelled on the linear actions, with the fixed point set of each transposition a codimension two homotopy sphere.A simple (2n – l)-knot is a differentiate embedding of a homotopy sphere K 2n–l into a homotopy sphere Σ2n+1 such that π j (Σ – K) = π j (S 1) for j < n. 
Liang, Chao-Chu. σ4-Actions On Homotopy Spheres. Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 275-281. doi: 10.4153/CJM-1981-022-7
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