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:
String bordism theory, $MString$, is bordism homology theory for manifolds equipped with string structure.
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:
Discussion of relation to the Witten genus:
Discussion of secondary characteristic classes in string cobordism cohomology theory and in tmf:
String bordism of the classifying space of $E_8$:
Discussion of geometric string bordism in degree 3 as a means to speak (via the Pontryagin-Thom theorem) about the third stable homotopy group of spheres:
Domenico Fiorenza, Eugenio Landi, Integrals detecting degree 3 string cobordism classes [arXiv:2209.12933]
Domenico Fiorenza, String bordism invariants in dimension 3 from $U(1)$-valued TQFTs, talk at QFT and Cobordism, CQTS (Mar 2023) [web]
Last revised on December 20, 2023 at 14:42:48. See the history of this page for a list of all contributions to it.