Evgeny Fominykh

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math.GT2016

Complexity of virtual 3-manifolds

Evgeny Fominykh, Vladimir Turaev, Andrei Vesnin

Virtual $3$ -manifolds were introduced by S.V. Matveev in 2009 as natural generalizations of the classical $3$ -manifolds. In this paper, we introduce a notion of complexity of a vir…

math.GT2010

Dehn surgeries on the figure eight knot: an upper bound for the complexity

Evgeny Fominykh

We establish an upper bound $ω (p / q)$ on the complexity of manifolds obtained by $p / q$ -surgeries on the figure eight knot. It turns out that if $ω (p / q) ⩽ 12$ , the bound is sh…