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Urs Würgler, Morava K-theories: a survey; in Algebraic topology Poznan 1989, 111–138, Lecture Notes in Math., 1474, Springer, Berlin, 1991; Mark Hovey, Neil P. Strickland, Morava K-theories and localisation. Mem. Amer. Math. Soc. 139 (666) 1999; Paul Goerss, (Pre-)sheaves of ring spectra over the moduli stack of formal group laws.
The original construction of tmf uses the obstruction theory of Hopkins, Miller, and Paul Goerss, and is based on ideas of Dwyer, Kan, and Stover.In this approach, one defines a presheaf O top ("top" stands for topological) of multiplicative cohomology theories on the etale site of the moduli stack of elliptic curves and shows that this can be lifted in an essentially unique way to a sheaf of ...
Together with Paul Goerss, Hopkins later set up a systematic obstruction theory for refinements to ... [14] [15] 2012 the NAS Award in Mathematics, ...
Paul Goerss, Hans-Werner Henn, Mark E. Mahowald, and Charles Rezk, A resolution of the K(2)-local sphere at the prime 3, Annals of Mathematics 162 (2005), 777–822. JSTOR 20159929; Prasit Bhattacharya, Philip Egger and Mark E. Mahowald, On the periodic v2-self-map of A1, Algebraic and Geometric Topology 17 (2017) 657–692.
She completed her Ph.D. in 2013, with the dissertation The Duality Resolution Spectral Sequence for the Moore Spectrum at the Prime 2 supervised by Paul Goerss. [ 3 ] After working at the University of Chicago from 2013 to 2016 as an L. E. Dickson Instructor in mathematics, she joined the Department of Mathematics at the University of Colorado ...
Call a cohomology theory even periodic if = for i odd and there is an invertible element .These theories possess a complex orientation, which gives a formal group law.A particularly rich source for formal group laws are elliptic curves.
Let : be a Serre fibration of topological spaces, and let F be the (path-connected) fiber.The Serre cohomology spectral sequence is the following: , = (, ()) + (). Here, at least under standard simplifying conditions, the coefficient group in the -term is the q-th integral cohomology group of F, and the outer group is the singular cohomology of B with coefficients in that group.
In mathematics, the Landweber exact functor theorem, named after Peter Landweber, is a theorem in algebraic topology. It is known that a complex orientation of a homology theory leads to a formal group law. The Landweber exact functor theorem (or LEFT for short) can be seen as a method to reverse this process: it constructs a homology theory ...