A mapping theorem for topological complexity

Mark Grant, Gregory Lupton, John Oprea

Research output: Contribution to journalArticle

3 Citations (Scopus)
4 Downloads (Pure)

Abstract

We give new lower bounds for the (higher) topological complexity of a space, in terms of the LusternikSchnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and more generally for the rational sectional category of a map, in terms of the rational category of a certain auxiliary space. We use our results to deduce consequences for the global (rational) homotopy structure of simply connected, hyperbolic finite complexes.
Original languageEnglish
Pages (from-to)1643-1666
Number of pages24
JournalAlgebraic & Geometric Topology
Volume15
Issue number3
Early online date19 Jun 2015
DOIs
Publication statusPublished - 19 Jun 2015

Fingerprint

Topological Complexity
Theorem
Rational Homotopy
Lusternik-Schnirelmann Category
Lower bound
Deduce

Keywords

  • Lusternik–Schnirelmann category
  • sectional category
  • topological complexity
  • topological robotics
  • sectioned fibration
  • connective cover
  • Avramov–Félix conjecture

Cite this

A mapping theorem for topological complexity. / Grant, Mark; Lupton, Gregory; Oprea, John.

In: Algebraic & Geometric Topology, Vol. 15, No. 3, 19.06.2015, p. 1643-1666.

Research output: Contribution to journalArticle

Grant, Mark ; Lupton, Gregory ; Oprea, John. / A mapping theorem for topological complexity. In: Algebraic & Geometric Topology. 2015 ; Vol. 15, No. 3. pp. 1643-1666.
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