Геометрия и комбинаторика виртуальных узлов (1097523), страница 62
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Òî, ÷òî ñðåäè çàìûêàíèé Êèøèíîóçëîâ Ki âñòðå÷àåòñÿ áåñêîíå÷íî ìíîãî ðàçëè÷íûõ óçëîâ, ñëåäóåò èç òîãî, ÷òî ýòè çàìûêàíèÿ ìîãóò èìåòü ëþáîé ñêîëü óãîäíî áîëüøîé íàïåðåäçàäàííûé ðîä.Ïîñëåäíåå óòâåðæäåíèå ñëåäóåò èç òîãî, ÷òî ñîîòâåòñòâóþùèå âèðòóàëüíûå óçëû èìåþò ñêîëü óãîäíî áîëüøîé íàïåðåä çàäàííûé ðîä â ïëîñêîéêàòåãîðèè, ò.å.
åñëè ìû ðàçðåøèì ïîìèìî îáîáùåííûõ äâèæåíèé åéäåìåéñòåðà ïðèìåíÿòü çàìåíó òèïîâ êëàññè÷åñêèõ ïåðåêðåñòêîâ (ò.å. áóäåìðàáîòàòü ñ âèðòóàëüíûìè óçëàìè ñ òî÷íîñòüþ äî èíâàðèàíòîâ Âàñèëüåâàïîðÿäêà 0). À èìåííî, îïðåäåëÿÿ ïî äèàãðàììå Ki ïîâåðõíîñòü ñ ñèñòåìîé êðèâûõ â íåé ìû ïîëó÷èì ìèíèìàëüíóþ ðåàëèçàöèþ (íå èìåþùóþ íèïåòåëü, íè äâóóãîëüíèêîâ).8.7. Áåñêîíå÷íîñòü êîëè÷åñòâà äëèííûõ óçëîâ,èìåþùèõ èêñèðîâàííîå çàìûêàíèåèñ.
8.14. Âîññòàíîâëåíèå ãðàà ïî d-äèàãðàììå3698.7. Áåñêîíå÷íîñòü êîëè÷åñòâà äëèííûõ óçëîâ,èìåþùèõ èêñèðîâàííîå çàìûêàíèåèñ. 8.15. Îòñóòñòâèå ñòðóêòóðû èñòî÷íèê-ñòîê âëå÷åò íåâëîæèìîñòü ñ ó÷åòîì A-ñòðóêòóðûèñ. 8.16. Îïåðàöèÿ′èñ. 8.17. Çàìûêàíèå Êèøèíî370ËèòåðàòóðàÏóáëèêàöèè àâòîðà ïî òåìå äèññåðòàöèè:[Ìà1℄ Ìàíòóðîâ, Â.Î.
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1113.Äî-[Ìà5℄ Ìàíòóðîâ, Â.Î. (2003), Àòîìû è ìèíèìàëüíûå äèàãðàììû âèðòóàëüíûõ çàöåïëåíèé, Äîêëàäû ÀÍ, 391 (2), ññ. 166168.[Ìà6℄ Ìàíòóðîâ, Â.Î. (2004), Ïîëèíîì Õîâàíîâà äëÿ âèðòóàëüíûõ óçëîâ,Äîêëàäû ÀÍ, 398, (1). ññ.15-18.[Ìà7℄ Ìàíòóðîâ, Â.Î. (2003), Êðèâûå íà ïîâåðõíîñòÿõ, âèðòóàëüíûå óçëûè ïîëèíîì Äæîíñà-Êàóìàíà, Äîêëàäû ÀÍ, 390 (2) ññ. 155-157.[Ìà8℄ Ìàíòóðîâ, Â.Î. (2004), Èíâàðèàíòû êîíå÷íîãî ïîðÿäêà âèðòóàëüíûõçàöåïëåíèé è ïîëèíîì Äæîíñà-Êàóìàíà, Äîêëàäû ÀÍ, 395 (1), .18-21.[Ìà9℄ Ìàíòóðîâ, Â.Î. (2005), Î äëèííûõ âèðòóàëüíûõ óçëàõ,ÀÍ, 401 (5), . 595-598.Äîêëàäû[Ìà10℄ Ìàíòóðîâ, Â.Î. (2002), Èíâàðèàíòíûé ïîëèíîì äâóõ ïåðåìåííûõäëÿ âèðòóàëüíûõ çàöåïëåíèé, Óñïåõè ìàò.
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