| Autor: |
J. H. Rieger, Sunayana Ghosh |
| Přispěvatelé: |
Wetenschappelijke Visualisatie en Computergrafiek |
| Jazyk: |
Dutch; Flemish |
| Rok vydání: |
2006 |
| Předmět: |
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| Zdroj: |
Geometriae dedicata, 121, 73-87. SPRINGER |
| ISSN: |
0046-5755 |
| Popis: |
The secant map of an immersion sends a pair of points to the direction of the line joining the images of the points under the immersion. The germ of the secant map of a generic codimension-c immersion \(X\!\!:{\mathbb R}^n \to {\mathbb R}^{n+c}\) at the diagonal in the source is a \({\mathbb Z}_2\) stable map-germ \({\mathbb R}^{2n} \to {\mathbb R}^{n+c-1}\) in the following cases: (i) c≥ 2 and (2n,n + c − 1) is a pair of dimensions for which the \({\mathbb Z}_2\) stable germs of rank at least n are dense, and (ii) for generically immersed surfaces (i.e., n = 2 and any c≥ 1). In the latter surface case the \({\mathcal A}^{{\mathbb Z}_2}\)-classification of germs of secant maps at the diagonal is described and it is related to the \({\mathcal A}\)-classification of certain singular projections of the surfaces. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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