nLab finite-dimensional complex orientation and Ravenel's spectra -- references

Finite-dimensional complex orientation and Ravenel’s spectra

Discussion of complex orientation (in Whitehead generalized cohomology) on (only) those complex vector bundles which are pulled back from base spaces of bounded cell-dimension (Hopkins 84, 1.2, Ravenel 86, 6.5.2) – or rather, for the most part, of Ravenel's Thom spectra $X(n)$ and $T(m)$ (Ravenel 84, Sec. 3) which co-represent these:

• Douglas Ravenel, section 3 of: Localization with Respect to Certain Periodic Homology Theories, American Journal of Mathematics Vol. 106, No. 2 (Apr., 1984), pp. 351-414 (doi:10.2307/2374308, jstor:2374308)

• Michael Hopkins, Stable decompositions of certain loop spaces, Northwestern 1984 (pdf)

• Douglas Ravenel, section 6.5 of: Complex cobordism and stable homotopy groups of spheres, 1986

• Ethan Devinatz, Michael Hopkins, Jeffrey Smith, Theorem 3 of: Nilpotence and Stable Homotopy Theory I, Annals of Mathematics Second Series, Vol. 128, No. 2 (Sep., 1988), pp. 207-241 (jstor:1971440)

• Doug Ravenel, The first Adams-Novikov differential for the spectrum $T(m)$, 2000 (pdf, pdf)

• Ippei Ichigi, Katsumi Shimomura, The Modulo Two Homotopy Groups of the $L_2$-Localization of the Ravenel Spectrum, CUBO A Mathematical Journal, Vol. 10, No 03, (43–55). October 2008 (cubo:1498)

• Gabe Angelini-Knoll, J. D. Quigley: The Segal Conjecture for topological Hochschild homology of the Ravenel spectra, Journal of Topology 4 3 (2011) 591-622 [doi:10.1112/jtopol/jtr015, arXiv:1705.03343]

• Jonathan Beardsley, A Theorem on Multiplicative Cell Attachments with an Application to Ravenel’s $X(n)$ Spectra, Journal of Homotopy and Related Structures volume 14, pages 611–624 (2019) (arXiv:1708.03042, doi:10.1007/s40062-018-0222-6)

• Jonathan Beardsley, Topological Hochschild homology of $X(n)$ (arXiv:1708.09486)

• Xiangjun Wang, Zihong Yuan, The homotopy groups of $L_2 T(m)/\big(p^{[\tfrac{m}{2}]+2}, v_1 \big)$ for $m \gt 1$, New York J. Math.24 (2018) 1123–1146 (pdf)