Definition of homotopy groups, homotopy theory of CW complexes, Huriewich theorem and Whitehead's theorem, Eilenberg-Maclane spaces, fibration and cofibration sequences, Postnikov towers, and obstruction theory. Prerequisite: MATH 7800.

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organizational meeting

Nick Kuhn (UVA) - Adams filtration and Hurewicz maps for infinite loopspaces

If X is an infinite loopspace, we relate the Adams filtration of its homotopy to the behavior of the Hurewicz map. As examples, we recover a famous result of Milnor about vector bundles over spheres, and prove an analogue for Topological Modular Forms.

I'll focus on explaining the theorem and examples. The proof needs as input new constructions in algebras over an operad, which is a joint project with Luis Pereira. (Maybe he will speak soon about this.)

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MATH 7840

Definition of homotopy groups, homotopy theory of CW complexes, Huriewich theorem and Whitehead's theorem, Eilenberg-Maclane spaces, fibration and cofibration sequences, Postnikov towers, and obstruction theory. Prerequisite: MATH 7800.