MSpinᶜ (changes) in nLab
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Context
Cobordism theory
cobordism theory = manifolds and cobordisms + stable homotopy theory/higher category theory
Concepts of cobordism theory
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Pontrjagin's theorem (equivariant, twisted):
↔\phantom{\leftrightarrow} Cohomotopy
↔\leftrightarrow cobordism classes of normally framed submanifolds
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↔\phantom{\leftrightarrow} homotopy classes of maps to Thom space MO
↔\leftrightarrow cobordism classes of normally oriented submanifolds
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complex cobordism cohomology theory
flavors of bordism homology theories/cobordism cohomology theories, their representing Thom spectra and cobordism rings:
bordism theory\;M(B,f) (B-bordism):
relative bordism theories:
global equivariant bordism theory:
algebraic:
Contents
Idea
The cobordism theory for manifolds equipped with (stable) Spin^c spinᶜ structure.
Properties
Atiyah-Bott-Shapiro orientation
(…)
see at Atiyah-Bott-Shapiro orientation
(…)
Relation to complex K-theory
MSpin cM Spin^c is related to KU in a variant of the Conner-Floyd isomorphism, via the Atiyah-Bott-Shapiro orientation (Hopkins-Hovey 92, Thm. 1)
flavors of bordism homology theories/cobordism cohomology theories, their representing Thom spectra and cobordism rings:
bordism theory\;M(B,f) (B-bordism):
relative bordism theories:
global equivariant bordism theory:
algebraic:
References
- Michael Hopkins, Mark Hovey, Spin cobordism determines real K-theory, Mathematische Zeitschrift volume 210, pages 181–196 (1992) (doi:10.1007/BF02571790, pdf)
Last revised on July 5, 2024 at 14:11:57. See the history of this page for a list of all contributions to it.