Folding maps and the surgery theory on manifolds

スポンサーリンク

概要

• 論文の詳細を見る

• Let f:N→ P be a smooth map between n-dimensional oriented manifolds which has only folding singularities. Such a map is called a folding map. We prove that a folding map f:N→ P canonically determines the homotopy class of a bundle map of TNoplusθ<SUB>N</SUB> to TPoplusθ<SUB>P</SUB>, where θ<SUB>N</SUB> and θ<SUB>P</SUB> are the trivial line bundles over N and P respectively. When P is a closed manifold in addition, we define the set Ω<SUB>fo1d</SUB>(P) of all cobordism classes of folding maps of closed manifolds into P of degree 1 under a certain cobordism equivalence. Let SG denote the space \displaystyle \lim<SUB>k→∞</SUB>SG<SUB>k</SUB>, where SG<SUB>k</SUB> denotes the space of all homotopy equivalences of S<SUP>k-1</SUP> of degree 1. We prove that there exists an important map of Ω<SUB>fo1d</SUB>(P) to the set of homotopy classes [P, SG]. We relate Ω<SUB>fo1d</SUB>(P) with the set of smooth structures on P by applying the surgery theory.

• 社団法人 日本数学会の論文

著者

• Ando Yoshifumi

  Department Of Mathematics Yamaguchi University

• Ando Yoshifumi

  Department Of Mathematical Sciences Faculty Of Science Yamaguchi University

関連論文

• On the elimination of Morin singularities
• Folding maps and the surgery theory on manifolds
• On the Higher Thom Polynomials of Morin Singularities : Dedicated to Professor H. Toda on his 60th birthday
• Existence theorems of fold-maps
• Elimination of certain Thom-Boardman singularities of order two
• The homotopy principle for maps with singularities of given K-invariant class
• Invariants of Fold-maps via Stable Homotopy Groups : Dedicated to Professor Tatsuo Suwa on his sixtieth birthday
• The homotopy type of the space consisting of regular jets and folding jets in J^2 (n, n)
• On thom polynomials of the singularities D_k nad E_k

スポンサーリンク