arXiv subjects

Andrzej Nagórko

Publications and source records attributed to Andrzej Nagórko.

3 recordsLinked to original sources

arXiv2016

Coarse property {C} and decomposition complexity

The coarse category was established by Roe to distill the salient features of the large-scale approach to metric spaces and groups that was started by Gromov. In this paper, we use the language of coarse spaces to define coarse versions of asymptotic property C and decomposition complexity. We prove that coarse property C implies coarse property A; we also show that these coarse versions share many of the features of their metric analogs such as preservation by products or unions.

math.GT↗

arXiv2007

Carrier and Nerve Theorems in the Extension Theory

We show that a regular cover of a general topological space provides structure similar to a triangulation. In this general setting we define analogues of simplicial maps and prove their existence and uniqueness up to homotopy. As an application we give simple proofs of sharpened versions of nerve theorems of K. Borsuk and A. Weil, which state that the nerve of a regular cover is homotopy equivalent to the underlying space. Next we prove a nerve theorem for a class of spaces with uniformly bounded extension dimension. In particular we prove that the canonical map from a separable metric n-dimensional space into the nerve of its weakly regular open cover induces isomorphisms on homotopy groups of dimensions less than n.

math.GN↗

arXiv2007

Characterization and topological rigidity of Nobeling manifolds

We develop a theory of Nobeling manifolds similar to the theory of Hilbert space manifolds. We show that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular, the Nobeling manifold characterization conjecture is proven.

math.GT↗