# References for the Felix Klein Lectures

Notes

http://www.math.uiuc.edu/~rezk/felix-klein-lectures-notes.pdf

General references

- A large collection of relevant references is the literature list prepared by Nora Ganter for the 2007 Talbot Workshop: http://math.umn.edu/~tlawson/tmf-mirror/
- Many references are listed in the nLab, including in http://ncatlab.org/nlab/show/elliptic+cohomology and http://ncatlab.org/nlab/show/tmf.
- Topological Modular Forms, AMS Surveys and Monographs, 2014, edited by Douglas, Francis, Henriques, and Hill.

Lecture 1: A brief introduction to elliptic cohomology: its origin in elliptic genera, and its relation to (derived) algebraic geometry

- Hirzebruch, Rainer, Jung, "Manifolds and Modular Forms", 1992/1994. This book contains a friendly introduction to elliptic genera following Ochanine and Witten.
- Goerss, "Topological Modular Forms [after Hopkins, Miller, and Lurie]", Seminaire Bourbaki 2008-9. An overview of the construction of the sheaf of elliptic spectra on the elliptic moduli stack. http://www.math.northwestern.edu/~pgoerss/papers/Exp.1005.P.Goerss.pdf
- Douglas, Francis, Henriques, Hill, "Topological modular forms", AMS Surveys and Monographs. Contains a detailed exposition of the Goerss-Hopkins-Miller construction of tmf. http://math.mit.edu/conferences/talbot/2007/tmfproc/
- Lurie, "A survey of elliptic cohomology", 2007. An exposition of his results. http://www.math.harvard.edu/~lurie/papers/survey.pdf

Lecture 2: Morava E-theory (generalized cohomology theories associated to universal deformations of formal groups) and its power operations

- Ando, "Isogenies of formal group laws and power operations in the cohomology theories E
_{n}", Duke Journal 1995. The original construction. - Ando, Hopkins, Strickland, "The sigma orientation is an H-infinity map", American J. Math 2004. Describes "descent for level structures", a slightly weaker variant of the "descent for isogenies" described in my talk. http://arxiv.org/abs/math/0204053
- Rezk, "The congruence criterion for power operations in Morava E-theory", HHA 2009. Gives an outline of the AHS theory of power operations, and describes the role of the "Frobenius congruence". http://arxiv.org/abs/0902.2499
- Rezk, "Power operations in Morava E-theory: structure and calculations (Draft)". Gives a summary of the theory, and describes some calculations at height 2. http://www.math.uiuc.edu/~rezk/power-ops-ht-2.pdf