nLab cyclic space

Idea

A cyclic space is a cyclic object in a category of spaces, usually in one of the standard presentations of homotopy types, hence in TopologicalSpaces or SimplicialSets.

Related concepts

• cyclic homology

• cyclic category

• cyclic object

• cyclic set

• cyclotomic space

• cyclotomic spectrum

References

• D. Burghelea Z. Fiedorowicz, Section 1 of: Cyclic homology and algebraic K-theory of spaces—II, Topology Volume 25, Issue 3, 1986, Pages 303-317 (doi:10.1016/0040-9383(86)90046-7)

• Jean-Louis Loday, Cyclic Spaces and $S^1$-Equivariant Homology (doi:10.1007/978-3-662-21739-9_7)

  Chapter 7 in: Cyclic Homology, Grundlehren 301, Springer 1992 (doi:10.1007/978-3-662-21739-9)

• Jean-Louis Loday, Section 3 of: Free loop space and homology, Chapter 4 in: Janko Latchev, Alexandru Oancea (eds.): Free Loop Spaces in Geometry and Topology, IRMA Lectures in Mathematics and Theoretical Physics 24, EMS 2015 (arXiv:1110.0405, ISBN:978-3-03719-153-8)

See also:

• Wikipedia, Cyclic category

In the context of geometric realization of loop stacks and inertia stacks:

• Ernesto Lupercio, Bernardo Uribe, Section 7.2 of: Inertia orbifolds, configuration spaces and the ghost loop space, Quarterly Journal of Mathematics 55 2 (2004) 185-201 (arxiv:math.AT/0210222, doi:10.1093/qmath/hag053)