Orbifold bordism and duality for finite orbispectra

John Pardon

Research output: Contribution to journalArticlepeer-review


We construct the stable (representable) homotopy category of finite orbispectra, whose objects are formal desuspensions of finite orbi-CW–pairs by vector bundles and whose morphisms are stable homotopy classes of (representable) relative maps. The stable representable homotopy category of finite orbispectra admits a contravariant involution extending Spanier–Whitehead duality. This duality relates homotopical cobordism theories (cohomology theories on finite orbispectra) represented by global Thom spectra to geometric (derived) orbifold bordism groups (homology theories on finite orbispectra). This isomorphism extends the classical Pontryagin–Thom isomorphism and its known equivariant generalizations.

Original languageEnglish (US)
Pages (from-to)1747-1844
Number of pages98
JournalGeometry and Topology
Issue number5
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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