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The coarse shape groups (CROSBI ID 158681)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Koceić-Bilan, Nikola The coarse shape groups // Topology and its applications, 157 (2010), 5; 894-901. doi: 10.1016/j.topol.2009.12.005

Podaci o odgovornosti

Koceić-Bilan, Nikola

engleski

The coarse shape groups

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.

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

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Podaci o izdanju

157 (5)

2010.

894-901

objavljeno

0166-8641

1879-3207

10.1016/j.topol.2009.12.005

Povezanost rada

Matematika

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