Topological triviality of a family of zero-sets
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- by Michael A. Buchner and Wojciech Kucharz PDF
- Proc. Amer. Math. Soc. 102 (1988), 699-705 Request permission
Abstract:
This paper gives conditions on a mapping $F:U \times {{\mathbf {R}}^k} \to {{\mathbf {K}}^p}\left ( {U \subset {{\mathbf {K}}^n}{\text {open, }}{\mathbf {K}} = {\mathbf {R}}\;{\text {or }}{\mathbf {C}}} \right )$ such that the family $F_t^{ - 1}\left ( 0 \right )$ is a topologically trivial family (i.e., does not change topologically as $t \in {{\mathbf {R}}^k}$ varies). As an application an easy proof is given of a counterexample to a conjecture of Thom concerning the number of topologically different realizations of a given jet.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 699-705
- MSC: Primary 58C25
- DOI: https://doi.org/10.1090/S0002-9939-1988-0929006-5
- MathSciNet review: 929006