cobordism theory = manifolds and cobordisms + stable homotopy theory/higher category theory
Concepts of cobordism theory
Pontrjagin's theorem (equivariant, twisted):
$\phantom{\leftrightarrow}$ Cohomotopy
$\leftrightarrow$ cobordism classes of normally framed submanifolds
$\phantom{\leftrightarrow}$ homotopy classes of maps to Thom space MO
$\leftrightarrow$ cobordism classes of normally oriented submanifolds
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:
The cobordism theory for manifolds equipped with (stable) Spin^c structure.
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see at Atiyah-Bott-Shapiro orientation
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$M Spin^c$ 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:
Created on February 18, 2021 at 09:53:45. See the history of this page for a list of all contributions to it.