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Klassifikacija vloženij torov v 2-metastabilʹnoj razmernostiRepovš, Dušan, 1954- ; Skopenkov, Mikhail, 1983- ; Cencelj, Matija, 1958-Članek je posvečen klasičnemu problemu vozlanja: za dano mnogoterost ▫$N$▫ in naravno število ▫$m$▫ opišite množico izotopnih razredov vložitev ▫$N\to S^m$▫. Posvetimo se posebnemu primeru zavozlanih ... torusov, to je vložitvam ▫$S^p \times S^q \to S^m$▫. Klasifikacijo zavozlanih torusov do izotopije so v metastabilnem območju ▫$m \geq p + \frac{3}{2}q + 2$▫, ▫$p \leq q$▫ podali A. Haefliger, E. Zeeman in A.B. Skopenkov. Tu obravnavamo dimenzije pod metastabilim območjem in najdemo eksplicitni kriterij za končnost množice izotopnih razredov v 2-metastabilnih dimenzijah: Izrek: Predpostavimo ▫$p + \frac{4}{3}q + 2 < m < p + \frac{3}{2}q + 2$▫ in ▫$m > 2p+q + 2$▫. Tedaj je množica izotopnih razredov gladkih vložitev ▫$S^p \times S^q \to S^m$▫ neskončna natanko tedaj, ko je ali ▫$q + 1$▫ ali pa ▫$p + q + 1$▫ deljivo s 4. Naš pristop h klasifikaciji temelji na analogu eksaktnega zaporedja U. Koschorkeja iz teorije spletov. V našem zaporedju nastopa nova ▫$\beta$▫-invarianta zavozlanih torusov. Eksaktnost dokažemo z vložitveno kirurgijo in tehnikami N. Habeggerja in U. Kaiserja.Source: Matematičeskij sbornik. - ISSN 0368-8666 (T. 203, no. 11, 2012, str. 129-158)Type of material - article, component partPublish date - 2012Language - russianCOBISS.SI-ID - 16435545
Author
Repovš, Dušan, 1954- |
Skopenkov, Mikhail, 1983- |
Cencelj, Matija, 1958-
Topics
matematika |
topologija |
zavozlani torus |
splet |
spletna preslikava |
vložitev |
kirurgija |
mathematics |
topology |
knotted torus |
link |
link map |
embedding |
surgery
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Repovš, Dušan, 1954- | 07083 |
Skopenkov, Mikhail, 1983- | ![]() |
Cencelj, Matija, 1958- | 03342 |
Source: Personal bibliographies
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