4 papers
Minimal quasisections of circle bundles
Ivan Kiselev, Gaiane Panina, Timur Shamazov
Let be an oriented circle bundle over an oriented closed surface, and let denote its Euler number. A \textit{quasisection} is a smooth surface , p…
Computing the Hopf invariant
Oleg R. Musin, Timur Shamazov
We consider Whitehead's integral formula and propose an algorithm for computing the Hopf invariant for simplicial mappings.
A new proof of Milnor-Wood inequality
Gaiane Panina, Timur Shamazov, Maksim Turevskii
The Milnor-Wood inequality states that if a (topological) oriented circle bundle over an orientable surface of genus has a smooth transverse foliation, then the Euler class of…
Quasisections of circle bundles and Euler class
Gaiane Panina, Timur Shamazov, Maksim Turevskii
Let be an oriented circle bundle over an oriented closed surface . A quasisection is a smooth surface (either closed or bordered) mapped by a…