21-st and 22-nd homotopy groups of the n-th rotation group

We denote by Rn the n-th rotatoin group and by πk(Rn) the k-th homotopy group of Rn. We determine the group structures of the homotopy groups πk(Rn) for k=21 and 22 by use of the fibration Rn₊₁ rn→Sⁿ.ArticleJournal of the Faculty of Science Shinshu University 41: 1-28(2007)departmental bulletin pape

COMPOSITIONS OF EQUI-DIMENSIONAL FOLD MAPS

Abstract. According to Ando's theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket in the stable stem through Ando's isomorphism. By using the operations we explicitly construct several fold maps with favourable properties, including a fold map which represents the generator of the stable 6-stem