An upper bound for topological complexity

Michael Farber, Mark Grant, Gregory Lupton, John Oprea (Corresponding Author)

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In [11], a new approximating invariant TCD for topological complexity was introduced called D-topological complexity. In this paper, we explore more fully the properties of TCD and the connections between TCD and invariants of Lusternik-Schnirelmann type. We also introduce a new TC-type invariant TCf that can be used to give an upper bound for TC,
TC(X) ≤ TCD (X) + 2dimX − k k + 1 ,
where X is a finite dimensional simplicial complex with k-connected universal cover X˜ . The above inequality is a refinement of an estimate given by Dranishnikov [5].
Original languageEnglish
Pages (from-to)109-125
Number of pages17
JournalTopology and its Applications
Early online date30 Jan 2019
Publication statusPublished - 15 Mar 2019

Bibliographical note

This work was partially supported by a grant from the Simons Foundation: (#244393 to John Oprea).

The authors would like to thank the Mathematisches Forschungsinstitut Oberwolfach for its generosity in supporting a July 2017 Research in Pairs stay where this work was begun.


  • topological complexity
  • Lusternik-Schnirelmann categogory
  • Lusternik–Schnirelmann category
  • Topological complexity


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