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Poor ideal three-edge triangulations are minimal
Evgeny Fominykh, Ekaterina Shumakova
It is known that an ideal triangulation of a compact -manifold with nonempty boundary is minimal if and only if it contains the minimum number of edges among all ideal triangula…
Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds
P. Cristofori, E. Fominykh, M. Mulazzani +1
The graph complexity of a compact 3-manifold is defined as the minimum order among all 4-colored graphs representing it. Exact calculations of graph complexity have been already pe…
Three-dimensional manifolds with poor spines
Evgeny Fominykh, Vladimir Turaev, Andrei Vesnin
A special spine of a three-manifold is said to be poor if it does not contain proper simple subpolyhedra. Using the Turaev-Viro invariants, we establish that every compact three-di…
Upper bounds for the complexity of torus knot complements
Evgeny Fominykh, Bert Wiest
We establish upper bounds for the complexity of Seifert fibered manifolds with nonempty boundary. In particular, we obtain potentially sharp bounds on the complexity of torus knot…
Exact values of complexity for Paoluzzi - Zimmermann manifolds
Evgeny Fominykh, Andrei Vesnin
There are found exact values of (Matveev) complexity for the 2-parameter family of hyperbolic 3-manifolds with boundary constructed by Paoluzzi and Zimmermann. Moreover, -invari…