Volume 10 (2007)

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Hypersurface representation and the image of the double S³–transfer

Mitsunori Imaoka

Geometry & Topology Monographs 10 (2007) 187–193

DOI: 10.2140/gtm.2007.10.187

arXiv: 0903.4474

Abstract

We study the image of a transfer homomorphism in the stable homotopy groups of spheres. Actually, we show that an element of order 8 in the 18 dimensional stable stem is in the image of a double transfer homomorphism, which reproves a result due to P J Eccles that the element is represented by a framed hypersurface. Also, we determine the image of the transfer homomorphism in the 16 dimensional stable stem.

Keywords

transfer map, stable homotopy, hypersurface

Mathematical Subject Classification

Primary: 55R12

Secondary: 55Q45

References
Publication

Received: 24 August 2004
Revised: 5 July 2005
Published: 29 January 2007

Authors
Mitsunori Imaoka
Department of Mathematics Education
Graduate School of Education
Hiroshima University
1–1–1 Kagamiyama
Higashi–Hiroshima 739-8524
Japan