Enchiridion: Vol. 2 (2016): Vitaly Lorman

Vitaly Lorman (Johns Hopkins University)

User’s Guide
Topic 1: Key insights and organizing principles
Topic 2: Conceptual metaphors and mental imagery
Topic 3: Story of the development
Topic 4: Colloquial summary
(as a single PDF)

Source Paper
Landweber flat real pairs and ER(n)-cohomology
joint with Nitu Kitchloo and W. Stephen Wilson

Source Paper Abstract
We take advantage of the internal algebraic structure of the Bockstein spectral sequence converging to ER(n)^*(pt) to prove that for spaces Z that are part of Landweber flat real pairs with respect to E(n), the cohomology ring ER(n)^*(Z) can be obtained from E(n)^*(Z) by base change. In particular, our results allow us to compute the Real Johnson-Wilson cohomology of the Eilenberg-MacLane spaces Z = K(\mathbb{Z}, 2m+1), K(\mathbb{Z}/2^q, 2m), K(\mathbb{Z}/2, m) for all integers m and q, as well as connective covers of BO: BO, BSO, BSpin, and BO.

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