The Homotopy Category of Spectra.II.
The homotopy dimension of codiscrete subsets of the 2-sphere 𝕊²
Andreas Zastrow conjectured, and Cannon-Conner-Zastrow proved, that filling one hole in the Sierpiński curve with a disk results in a planar Peano continuum that is not homotopy equivalent to a 1-dimensional set. Zastrow's example is the motivation for this paper, where we characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopy equivalent to 1-dimensional compacta, we prove that each has fundamental group that...
The homotopy Lie algebra for finite complexes
The Idzik type quasivariational inequalities and noncompact optimization problems
The index of discontinuous vector fields.
The least number of fixed points of bimaps
The Lefschetz fixed point theorem for multivalued maps of non-metrizable spaces
The Lefschetz fixed point theorem for some noncompact multi-valued maps
The Lefschetz-Hopf theorem and axioms for the Lefschetz number.
The Leray-Schauder index and the fixed point theory for arbitrary ANRs
The Lyusternik-Shnirel'man category, vector bundles, and immersions of manifolds.
The minimizing of the Nielsen root classes
Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen...
The multicores in metric spaces and their application in fixed point theory
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.
The Nielsen coincidence theory on topological manifolds
We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.
The Nielsen product formula for coincidences
The Nilpotent Model for a Function Space
The obstruction to the deformation of a map out of a subspace [Book]
The product formula for Lusternik-Schnirelmann category.
The Product Formula for the Topological Degree of Strict ...-Contractions.
The Radius of Convergence of Poincaré Series of Loop Spaces.