Unstable v1-periodic Homotopy Groups through Goodwillie Calculus

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Date 23.09.2019
Hour 10:1511:15
Speaker Jens Kjaer, EPFL
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Category Conferences - Seminars

It is a classical result that the rational homotopy groups, $\pi_*(X) \otimes \mathbb{Q}$, as a Lie-algebra can be computed in terms of indecomposable elements of the rational cochains on $X$.
This result can also be recovered from applying Goodwillie calculus to rational homotopy theory.
A different simplification of the homotopy theory, is $v_h$-periodic homotopy theory. For $h = 1$ we are able to compute the K-theory based $v_1$-periodic Goodwillie spectral sequence in terms of derived indecomposables. This allows us to compute $v_1^{-1} \pi_* SU(d)$ in a very different way from the original computation by Davis.

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