Addendum to: A Bound for the Fixed-Point Index of an Area-Preserving Map with Applications to Mechanics.
Alexander duality, gropes and link homotopy.
Algebraic models of Poincaré embeddings.
Algebraic periods of self-maps of a rational exterior space of rank 2.
Algebraic properties of quasi-finite complexes
A countable CW complex K is quasi-finite (as defined by A. Karasev) if for every finite subcomplex M of K there is a finite subcomplex e(M) such that any map f: A → M, where A is closed in a separable metric space X satisfying XτK, has an extension g: X → e(M). Levin's results imply that none of the Eilenberg-MacLane spaces K(G,2) is quasi-finite if G ≠ 0. In this paper we discuss quasi-finiteness of all Eilenberg-MacLane spaces. More generally, we deal with CW complexes with finitely many...
Algebraic theory of fundamental dimension [Book]
Algorithms for Nielsen type periodic numbers of maps with remnant on surfaces with boundary and on bouquets of circles I
In this paper and its sequel we present a method that, under loose restrictions, is algorithmic for calculating the Nielsen type numbers NΦₙ(f) and NPₙ(f) of self maps f of hyperbolic surfaces with boundary and also of bouquets of circles. Because self maps of these surfaces have the same homotopy type as maps on wedges of circles, and the Nielsen periodic numbers are homotopy type invariant, we need concentrate only on the latter spaces. Of course the results will then automatically apply...
An algebraic method for calculating the topological degree
An Application of the Stiefel-Whitney Classes to the Proof of a Fixed Point Theorem for Set-Valued Mappings
We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.
An effective criterion for the existence of a mass partition
An Efficient Degree-Computation Method for a Generalized Method of Bisection.
An indecomposable -complex. II.
An index and a Nielsen number for n-valued multifunctions
An infinitary version of Sperner's Lemma
We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.
An Ulam stability result on quasi-b-metric-like spaces
In this paper a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.
Anosov theorem for coincidences on nilmanifolds
Suppose that L, L’ are simply connected nilpotent Lie groups such that the groups and in their lower central series have the same dimension. We show that the Nielsen and Lefschetz coincidence numbers of maps f,g: Γ∖L → Γ’∖L’ between nilmanifolds Γ∖L and Γ’∖L’ can be computed algebraically as follows: L(f,g) = det(G⁎ - F⁎), N(f,g) = |L(f,g)|, where F⁎, G⁎ are the matrices, with respect to any preferred bases on the uniform lattices Γ and Γ’, of the homomorphisms between the Lie algebras , ’ of...
Applications of knot theory in fluid mechanics
In this paper we present an overview of some recent results on applications of knot theory in fluid mechanics, as part of a new discipline called `topological fluid mechanics' (TFM). The choice of the topics covered here is deliberately restricted to those areas that involve mainly a combination of ideal fluid mechanics techniques and knot theory concepts, complemented with a brief description of some other concepts that have important applications in fluid systems. We begin with the concept of...
Applications of Nielsen theory to dynamics
In this talk, we shall look at the application of Nielsen theory to certain questions concerning the "homotopy minimum" or "homotopy stability" of periodic orbits under deformations of the dynamical system. These applications are mainly to the dynamics of surface homeomorphisms, where the geometry and algebra involved are both accessible.
Approximable dimension and acyclic resolutions
Asymptotic dimension of coarse spaces.