Naslov
The coarse shape groups

Autori
Koceić-Bilan, Nikola

Izvornik
Topology and its applications (0166-8641) 157 (2010), 5; 894-901

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
topological space ; polyhedron ; inverse system ; pro-category ; pro∗-category ; expansion ; shape ; coarse shape ; homotopy pro-group ; shape group ; n-shape connectedness

Sažetak
The (pointed) coarse shape category Sh* (Sh(star)*), having (pointed) topological spaces as objects and having the (pointed) shape category as a subcategory. was recently constructed. Its isomorphisms classify (pointed) topological spaces strictly coarser than the (pointed) shape type classification. In this paper we introduce a new algebraic coarse shape invariant which is an invariant of shape and homotopy, as well. For every pointed space (X, star) and for every k is an element of N-0, the coarse shape group pi(k)* (X, star), having the standard shape group pi(k)(X, star) for its subgroup, is defined. Furthermore, a functor pi(k)* : Sh(star)* --> Grp is constructed. The coarse shape and shape groups already differ on the class of polyhedra. An explicit formula for computing coarse shape groups of polyhedra is given. The coarse shape groups give us more information than the shape groups. Generally, pi(k)(X, star) = 0 does not imply pi(k)*(X, star) = 0 (e.g. for solenoids), but from pro-pi(k)(X, star) = 0 follows pi(k)*(X, star) = 0. Moreover, for pointed metric compacta (X, star), the n-shape connectedness is characterized by pi(k)*(X, star) = 0, for every k <= n. (C) 2009 Elsevier B.V. All rights reserved.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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