algebraic topology – application of higher algebra and higher category theory to the study of (stable) homotopy theory
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 page compiles material related to the book
The Relation of Cobordism to K-Theories,
Lecture Notes in Mathematics 28 Springer 1966
on cobordism theory and topological K-theory, meeting in the notion of the e-invariant.
projective spaces, in particular quaternionic projective space
(Landweber exact functor theorem for KU and KSp?, see also cobordism theory determining homology theory)
Last revised on February 21, 2021 at 11:14:26. See the history of this page for a list of all contributions to it.