Iterated wreath product of the simplex category and iterated loop spaces

By C. Berger. 2005

112 citations recorded by the source corpus.

Generalising Segal's approach to 1-fold loop spaces, the homotopy theory of n-fold loop spaces is shown to be equivalent to the homotopy theory of reduced Tn-spaces, where Tn is an iterated wreath product of the simplex category. A sequence of functors from Tn to G allows for an alternative description of the Segal spectrum associated to a G-space. This yields a canonical reduced Tn-set model for each Eilenberg?MacLane space.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/02213a401fdd20356d169c5cd5844f6d46d5fa52

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On an extension of the notion of Reedy category (2008, background): “[5,36]), is a morphism of generalized Reedy categories.”
The cobordism hypothesis (2017, background): “r Bun exists and the ∞-category cBunτ over cBun exists. 10 2.3. Flagged higher categories and Segal sheaves. We now deﬁne Joyal’s category Θn, the n-fold wreath product of the simplex category ∆: see [Be], [Re2], and §3.5 of [AFR2]. Denote Fin∗ := Fin ∗/ for the category of based ﬁnite sets; each ob”
From operator categories to higher operads (2013, unknown): “The previous result now immediately implies that the Leinster category of the iterated wreath productO coincides with Berger’s iterated wreath product (∆ ≀∆ ≀ · · · ≀∆) [7].”