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On Virtual Crossing Numbers for Virtual Knots
Knot virtual knot graph crossing number parity
2011/9/20
Abstract: The aim of the present paper is to prove that the minimal number of virtual crossings for some families of virtual knots grows quadratically with respect to the minimal number of classical c...
A Generalization of Turaev's Virtual String Cobracket
Turaev's Virtual String Cobracket Geometric Topology
2011/9/19
Abstract: In a previous paper, we defined an operation $\mu$ that generalizes Turaev's cobracket for loops on a surface. We showed that, in contrast to the cobracket, this operation gives a formula fo...
Motivic Milnor fibers over complete intersection varieties and their virtual Betti numbers
Motivic Milnor fibers complete intersection varieties their virtual Betti numbers
2010/11/26
We study the Jordan normal forms of the local and global monodromies over complete intersection subvarieties of Cn by using the theory of motivic Milnor fibers.The results will be explicitly described...