25 citations · 26 across the 3 of their papers we have counts for
3 papers
math.GT2009★ 1 cited
Cobordisms of Free Knots and Gauss Words
Denis Petrovich Ilyutko, Vassily Olegovich Manturov
We investigate cobordisms of free knots. Free knots and links are also called homotopy classes of Gauss words and phrases. We define a new strong invariant of free knots which allo…
math.GT2009
On Free Knots
Vassily Olegovich Manturov
We prove that for some knot-like objects one can easily recognize non-equivalence w.r.t. all Reidemeister moves by studying some equivalence classes modulo only 2nd Reidemeister mo…
math.GT2009★ 25 cited
On Free Knots and Links
Vassily Olegovich Manturov
Both classical and virtual knots arise as formal Gauss diagrams modulo some abstract moves corresponding to Reidemeister moves. If we forget about both over/under crossings structu…