Lie algebras and $v_n$-periodic spaces
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In this article, a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in $v_n$-periodic homots is considered.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.read more
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Higher Topos Theory
TL;DR: In this paper, a general introduction to higher category theory using the formalism of "quasicategories" or "weak Kan complexes" is provided, and a few applications to classical topology are included.
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Infinitesimal computations in topology
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
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Operads, homotopy algebra and iterated integrals for double loop spaces
Ezra Getzler,John D. S. Jones +1 more
TL;DR: In this paper, the authors provide some background to the theory of operads, used in the first author's papers on 2D topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th /9305013).