Lie algebras and $v_n$-periodic spaces

Gijs Heuts

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arXiv · 1803.06325

Lie algebras and $v_n$-periodic spaces

Gijs Heuts

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Abstract

We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in $v_n$-periodic homotopy groups. The case n = 0 corresponds to rational homotopy theory. In analogy with Quillen's results in the rational case, we prove that this $v_n$-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in T(n)-local spectra. We also compare it to the homotopy theory of commutative coalgebras in T(n)-local spectra, where it turns out there is only an equivalence up to a certain convergence issue of the Goodwillie tower of the identity.

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BibTeX RIS

Gijs Heuts. 2018-03-16. Lie algebras and $v_n$-periodic spaces. https://arxiv.org/abs/1803.06325

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