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:
This entry is about the article
Quelques propriétés globales des variétés différentiables
Comment. Math. Helv. 28, (1954). 17-86
on differential topology, proving Thom's theorem which identifies cobordism classes of normally oriented submanifolds with homotopy classes of maps into a universal Thom space $M SO(n)$.
Together with
or rather its belated exposition in
due to which Thom’s construction came to be mainly known as the Pontryagin-Thom construction, this lays the foundations of cobordism theory as such and as a tool in stable homotopy theory.
normally oriented submanifold (p. 67)
Pontryagin-Thom collapse (p. 69)
cobordism classes of submanifolds (p. 71)
Last revised on February 3, 2021 at 09:13:00. See the history of this page for a list of all contributions to it.