Compositions of equi-dimensional fold maps

Volume 216 / 2012

Yoshihiro Hirato, Masamichi Takase Fundamenta Mathematicae 216 (2012), 119-128 MSC: Primary 57R45; Secondary 55Q45, 57R35, 55Q35. DOI: 10.4064/fm216-2-3


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 these operations we explicitly construct several fold maps with convenient properties, including a fold map which represents the generator of the stable $6$-stem.


  • Yoshihiro HiratoDepartment of General Education
    Nagano National College of Technology
    716 Tokuma
    Nagano, 381-8550 Japan
  • Masamichi TakaseFaculty of Science and Technology
    Seikei University
    3-3-1 Kichijoji-kitamachi, Musashino
    Tokyo, 180-8633 Japan

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