PARITY AND PROJECTION FROM VIRTUAL KNOTS TO CLASSICAL KNOTS

被引：24
|
作者：
Manturov, Vassily Olegovich [1 ]
机构：
[1] Peoples Friendship Univ Russia, Moscow 117198, Russia
来源：
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2013年 / 22卷 / 09期
关键词：
Knot; virtual knot; surface; group; projection; crossing; crossing number; bridge number; INVARIANTS;
D O I：
10.1142/S0218216513500442
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct various functorial maps (projections) from virtual knots to classical knots. These maps are defined on diagrams of virtual knots; in terms of Gauss diagram each of them can be represented as a deletion of some chords. The construction relies upon the notion of parity. As corollaries, we prove that the minimal classical crossing number for classical knots. Such projections can be useful for lifting invariants from classical knots to virtual knots. Different maps satisfy different properties.
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页数：20
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