M. M. Postnikov: his life, work and legacy
Mapping theorems for compacta with an arbitrary involution
Mappings with 1-dimensional absolute neighborhood retract fibers
Maps into the torus and minimal coincidence sets for homotopies
Let X,Y be manifolds of the same dimension. Given continuous mappings , i = 0,1, we consider the 1-parameter coincidence problem of finding homotopies , 0 ≤ t ≤ 1, such that the number of coincidence points for the pair is independent of t. When Y is the torus and f₀,g₀ are coincidence free we produce coincidence free pairs f₁,g₁ such that no homotopy joining them is coincidence free at each level. When X is also the torus we characterize the solution of the problem in terms of the Lefschetz...
Maximal elements and equilibria of generalized games for -majorized and condensing correspondences.
Measurable cardinals and fundamental groups of compact spaces
We prove that all groups can be realized as fundamental groups of compact spaces if and only if no measurable cardinals exist. If the cardinality of a group G is nonmeasurable then the compact space K such that G = π₁K may be chosen so that it is path connected.
Merging of degree and index theory.
Méthodes homologiques dans la théorie des applications et des champs de vecteurs sphériques dans les espaces de Banach [Book]
Minimal atlases of manifolds
Minimal component numbers of fixed point sets
Let f: (X,A) → (X,A) be a relative map of a pair of compact polyhedra. We introduce a new relative homotopy invariant , which is a lower bound for the component numbers of fixed point sets of the self-maps in the relative homotopy class of f. Some properties of are given, which are very similar to those of the relative Nielsen number N(f;X,A).
Minimal Coverings of Manifolds with Balls.
Minimal fixed point sets of relative maps
Let f: (X,A) → (X,A) be a self map of a pair of compact polyhedra. It is known that f has at least N(f;X,A) fixed points on X. We give a sufficient and necessary condition for a finite set P (|P| = N(f;X,A)) to be the fixed point set of a map in the relative homotopy class of the given map f. As an application, a new lower bound for the number of fixed points of f on Cl(X-A) is given.
Minimal Nielsen root classes and roots of liftings.
Minimal number of periodic points for smooth self-maps of S³
Let f be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3 and r a fixed natural number. A topological invariant , introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of r-periodic points for all smooth maps homotopic to f. In this paper we calculate for all self-maps of S³.
Minimal periods of maps of rational exterior spaces
The problem of description of the set Per(f) of all minimal periods of a self-map f:X → X is studied. If X is a rational exterior space (e.g. a compact Lie group) then there exists a description of the set of minimal periods analogous to that for a torus map given by Jiang and Llibre. Our approach is based on the Haibao formula for the Lefschetz number of a self-map of a rational exterior space.
Minimal Seifert manifolds.
Minimal surface maps, fixed point indices and a Jiang-Guo type inequality
Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
Let f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the...
Multifractal analysis of nearly circular Julia set and thermodynamical formalism
Multiple solutions of the forced double pendulum equation