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2013 | 221 | 1 | 69-82
Tytuł artykułu

Covering maps over solenoids which are not covering homomorphisms

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let Y be a connected group and let f: X → Y be a covering map with the total space X being connected. We consider the following question: Is it possible to define a topological group structure on X in such a way that f becomes a homomorphism of topological groups. This holds in some particular cases: if Y is a pathwise connected and locally pathwise connected group or if f is a finite-sheeted covering map over a compact connected group Y. However, using shape-theoretic techniques and Fox's notion of an overlay map, we answer the question in the negative. We consider infinite-sheeted covering maps over solenoids, i.e. compact connected 1-dimensional abelian groups. First we show that an infinite-sheeted covering map f: X → Σ with a total space being connected over a solenoid Σ does not admit a topological group structure on X such that f becomes a homomorphism. Then, for an arbitrary solenoid Σ, we construct a connected space X and an infinite-sheeted covering map f: X → Σ, which provides a negative answer to the question.
Słowa kluczowe
Rocznik
Tom
221
Numer
1
Strony
69-82
Opis fizyczny
Daty
wydano
2013
Twórcy
autor
  • Department of Mathematics, Waseda University, Okubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan
  • Department of Mathematics, University of Split, Teslina 12, 21000 Split, Croatia
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm221-1-3
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