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Pregled bibliografske jedinice broj: 490724

Zbornik radova

Autori: Koceić Bilan, Nikola
Naslov: The coarse shape groups
Izvornik: Nafpaktos :
Skup: 2010 International conference on Topology and its Applications
Mjesto i datum: Nafpaktos, Grčka, 26-30.06.2010.
Ključne riječi: shape; coarse shape; shape group; hmotopy pro-group
Sažetak:
Coarse shape isomorphisms preserve some important topological invariants as connectedness, (strong) movability, shape dimension and stability. There are also several new algebraic coarse shape invariants. In this talk we introduce a new algebraic coarse shape invariant which is an invariant of shape and homotopy, as well. For every pointed space (X, ⋆) and for every k∈N₀, the coarse shape group π_{; ; k}; ; ^{; ; ∗}; ; (X, ⋆), having the standard shape group π_{; ; k}; ; (X, ⋆) for its subgroup, is defined. Furthermore, a functor π_{; ; k}; ; ^{; ; ∗}; ; :Sh_{; ; ⋆}; ; ^{; ; ∗}; ; →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, π_{; ; k}; ; (X, ⋆)=0 does not imply π_{; ; k}; ; ^{; ; ∗}; ; (X, ⋆)=0 (e.g. for solenoids), but from pro-π_{; ; k}; ; (X, ⋆)=0 follows π_{; ; k}; ; ^{; ; ∗}; ; (X, ⋆)=0. Moreover, for pointed metric compacta (X, ⋆), the n-shape connectedness is characterized by π_{; ; k}; ; ^{; ; ∗}; ; (X, ⋆)=0, for every k≤n.
Vrsta sudjelovanja: Predavanje
Vrsta prezentacije u zborniku: Sažetak
Vrsta recenzije: Međunarodna recenzija
Projekt / tema: 177-0372791-0886
Izvorni jezik: ENG
Kategorija: Znanstveni
Znanstvena područja:
Matematika
Upisao u CROSBI: koceic@pmfst.hr (koceic@pmfst.hr), 10. Stu. 2010. u 23:00 sati



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