cobordism theory = manifolds and cobordisms + stable homotopy theory/higher category theory
Concepts of cobordism theory
flavors of cobordism homology/cohomology theories and representing Thom spectra
(…)
flavors of bordism homology theories/cobordism cohomology theories, their representing Thom spectra and cobordism rings:
bordism theory$\,M B$ (B-bordism):
relative bordism theories:
global equivariant bordism theory:
algebraic:
Michael Atiyah, Bordism and Cobordism, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 57, Issue 2, April 1961, pp. 200 - 208 (doi:10.1017/S0305004100035064, pdf)
Sergei Novikov, Homotopy properties of Thom complexes, Mat. Sbornik 57 (1962), no. 4, 407–442, 407–442 (pdf, pdf)
Robert Stong, Chapter IX of: Notes on Cobordism theory, Princeton University Press, 1968 (toc pdf, ISBN:9780691649016, pdf)
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