25 citations · 83 across the 18 of their papers we have counts for
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Free Knos are Not Invertible
Vassily Olegovich Manturov
By using parity arguments we prove that free knots are, generally, not invertible.
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…
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…
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…