A study of the Ganea conjecture for topological complexity by using weak topological complexity

In this paper, we provide sufficient conditions for a space X to satisfy the Ganea conjecture for topological complexity. To achieve this, we employ two auxiliary invariants: weak topological complexity in the sense of Berstein–Hilton, along with a certain stable version of it. Several examples are...

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Published inMathematical proceedings of the Cambridge Philosophical Society Vol. 177; no. 2; pp. 241 - 261
Main Authors GARCIA-CALCINES, J. M., VANDEMBROUCQ, L.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2024
Subjects
Complexity
Equality
Topology
55Q25
55P99
55M30
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ISSN0305-0041
1469-8064
DOI10.1017/S0305004124000215

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Abstract In this paper, we provide sufficient conditions for a space X to satisfy the Ganea conjecture for topological complexity. To achieve this, we employ two auxiliary invariants: weak topological complexity in the sense of Berstein–Hilton, along with a certain stable version of it. Several examples are discussed.
AbstractList In this paper, we provide sufficient conditions for a space X to satisfy the Ganea conjecture for topological complexity. To achieve this, we employ two auxiliary invariants: weak topological complexity in the sense of Berstein–Hilton, along with a certain stable version of it. Several examples are discussed.
Author GARCIA-CALCINES, J. M.
VANDEMBROUCQ, L.
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  email: jmgarcal@ull.edu.es
  organization: Departamento de Matemáticas, Estadística e I.O., e IMAULL, Universidad de La Laguna, 38271 La Laguna, Spain. e-mail: jmgarcal@ull.edu.es
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  fullname: VANDEMBROUCQ, L.
  email: lucile@math.uminho.pt
  organization: Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal. e-mail: lucile@math.uminho.pt
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Cites_doi 10.1090/S0002-9947-1990-0956033-8
10.1016/S0040-9383(99)00047-6
10.1007/s00209-012-1061-5
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10.1112/jlms/jdq048
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10.2140/agt.2012.12.1789
10.1016/S0040-9383(02)00007-1
10.1007/s00454-002-0760-9
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10.1093/qmath/haz019
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10.1007/BF01303636
10.1016/0040-9383(91)90006-P
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SubjectTerms Complexity
Equality
Topology
Title A study of the Ganea conjecture for topological complexity by using weak topological complexity
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