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Effective topological complexity of spaces with symmetries

Zbigniew Błaszczyk and Marek Kaluba

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We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant, Dranishnikov, and Lubawski-Marzantowicz. In particular, it is bounded from above by Farber's topological complexity.

Article information

Publ. Mat., Volume 62, Number 1 (2018), 55-74.

Received: 16 March 2016
Revised: 10 June 2016
First available in Project Euclid: 16 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space 68T40: Robotics [See also 93C85]

equivariant topological complexity motion planning problem


Błaszczyk, Zbigniew; Kaluba, Marek. Effective topological complexity of spaces with symmetries. Publ. Mat. 62 (2018), no. 1, 55--74. doi:10.5565/PUBLMAT6211803.

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