1982
DOI: 10.2969/jmsj/03420241
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Elimination of certain Thom-Boardman singularities of order two

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Cited by 17 publications
(12 citation statements)
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“…We have chosen V to be parallelizable. This is justified by the following lemma and codimΣ 3 (n + 1, n + 1) = 9. By the definition of τ ( V , T (f )) in the case ∂V = S n , T (f ) yields the section of Ω 1 (τ ( V , T (f )), ε n+2 V )| CS n , which we denote by s T (f ) .…”
Section: Stable Maps Of Spheresmentioning
confidence: 99%
“…We have chosen V to be parallelizable. This is justified by the following lemma and codimΣ 3 (n + 1, n + 1) = 9. By the definition of τ ( V , T (f )) in the case ∂V = S n , T (f ) yields the section of Ω 1 (τ ( V , T (f )), ε n+2 V )| CS n , which we denote by s T (f ) .…”
Section: Stable Maps Of Spheresmentioning
confidence: 99%
“…It is known that c(Σ 2i , τ N − f * (τ P )) is equal modulo 2-torsion to the determinant of the i × i matrix whose (s, t) component is the Pontrjagin class p i+s−t (τ N − f * (τ P )) ( [21] and [2,Proposition 5.4]). The following proposition follows from Propositions 1.1 and 1.2.…”
Section: Proposition 12 (Du Plessismentioning
confidence: 99%
“…Proposition 1.1. (Ando [2]) Let n be a natural number. If there exists a natural number i such that i 3 − i 2 2n 2i 2 , then we have that Cl(Σ i (n, n)) ⊂ Uns(n, n).…”
Section: Nonexistence Conditionsmentioning
confidence: 99%
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“…The most easily computed part of an obstruction to the existence of such sections is the Thom polynomial, which is the homology class represented by the closure of the set Σ(f ) of the singular points of f of type Σ [22,36]. In fact, in some cases, it is shown that the vanishing of the Thom polynomial implies the existence of maps homotopic to f without the prescribed singularities [2,3,26]. However, the topological location of Σ(f ) in M can be non-trivial even if the Thom polynomial of Σ vanishes.…”
Section: Introductionmentioning
confidence: 99%