TY - JOUR
T1 - Orbifold bordism and duality for finite orbispectra
AU - Pardon, John
N1 - Publisher Copyright:
© 2023 MSP (Mathematical Sciences Publishers).
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
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U2 - 10.2140/gt.2023.27.1747
DO - 10.2140/gt.2023.27.1747
M3 - Article
AN - SCOPUS:85167573336
SN - 1465-3060
VL - 27
SP - 1747
EP - 1844
JO - Geometry and Topology
JF - Geometry and Topology
IS - 5
ER -