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
The refinement of bordism homology theory to equivariant stable homotopy theory.
flavors of bordism homology theories/cobordism cohomology theories, their representing Thom spectra and cobordism rings:
relative bordism theories:
global equivariant bordism theory:
algebraic:
Original discussion of equivariant cobordism classes of manifolds:
Pierre Conner, Edwin Floyd, Differentiable periodic maps, Bull. Amer. Math. Soc. Volume 68, Number 2 (1962), 76-86 (euclid:bams/1183524501)
Pierre Conner, Edwin Floyd, Maps of Odd Period, Annals of Mathematics, Second Series, Vol. 84, No. 2 (1966), pp. 132-156 (jstor:1970515)
Robert Stong, Unoriented Bordism and Actions of Finite Groups, Memoirs AMS 103, American Mathematical Society, 1970 (ams:memo-1-103/4)
Original discussion of equivariant Thom spectra:
Tammo tom Dieck, Kobordismentheorie und Transformationsgruppen, Aaarhus University Preprint Series 1968/69, No. 30 (gbooks)
Tammo tom Dieck, Bordism of -manifolds and integrality theorems, Topology Volume 9, Issue 4, November 1970, Pages 345-358 (doi:10.1016/0040-9383(70)90058-3)
Original discussion of the relation between equivariant bordism classes of manifolds and equivariant Thom spectra:
Arthur Wasserman, section 3 of Equivariant differential topology, Topology Vol. 8, pp. 127-150, 1969 (pdf)
Theodor Bröcker, Edward Hook, Stable equivariant bordism, Math Z 129, 269–277 (1972) (doi:10.1007/BF01187353)
Edward Hook, Equivariant cobordism and duality, Trans. Amer. Math. Soc. 178 (1973), 241-258 (doi:10.1090/S0002-9947-1973-0321120-4)
Tammo tom Dieck, Orbittypen und äquivariante Homologie II, Arch. Math. 26 (1975), no. 6, 650–662 (pdf)
Bernhard Hanke, Geometric versus homotopy theoretic equivariant bordism, Math. Ann. 332, 677–696 (2005) (arXiv:math/0412550, doi:10.1007/s00208-005-0648-0)
Survey:
Discussion in global equivariant homotopy theory is in
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