Critical points of invariant functions on closed orientable surfaces
Copyright policy )Critical points of invariant functions on closed orientable surfaces
In this paper, the authors study orientation-preserving actions of finite groups on closed orientable surfaces. The first part of their work consists of a description of the gradient field of an equivariant \(C^1\)-function and of an elementary, differential proof of the Riemann-Hurwitz formula. In a second part, they consider the equivariant Lusternik-Schnirelmann category and prove that it equals, with a few exceptions, the number of singular orbits of the action. They also show that the upper bound given by \textit{H. Colman} [Contemp. Math. 316, 35--40 (2002; Zbl 1035.55003)] is sharp in the case of preserving orientation actions on surfaces.
- Polish Academy of Sciences Poland
- Adam Mickiewicz University in Poznań Poland
- University of Agriculture Nigeria
- University of Agriculture Faisalabad Pakistan
- University of Gdańsk Poland
critical orbits, Riemann surfaces, Riemann-Hurwitz ramification formula, Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects), Compact Riemann surfaces and uniformization, Equivariant Lusternik-Schnirelmann category, invariant function, Finite group action, Finite groups of transformations in algebraic topology (including Smith theory), finite group action, equivariant Lusternik-Schnirelmann category
critical orbits, Riemann surfaces, Riemann-Hurwitz ramification formula, Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects), Compact Riemann surfaces and uniformization, Equivariant Lusternik-Schnirelmann category, invariant function, Finite group action, Finite groups of transformations in algebraic topology (including Smith theory), finite group action, equivariant Lusternik-Schnirelmann category
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