Operads and Cosimplicial Objects: An Introduction

By James E. McClure, Jeffrey H. Smith. 2004

46 citations recorded by the source corpus.

This paper is an introduction to the series of papers [26, 28, 29, 30], in which we develop a combinatorial theory of certain important operads and their actions.1 The operads we consider are A ∞ operads, E ∞ operads, the little n-cubes operad and the framed little disks operad. Sections 2, 6 and 9, which can be read independently, are an introduction to the theory of operads.

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

View Paper: https://www.semanticscholar.org/paper/1ec36bc8c1385401a634baabe41ebe6cd5684e9b

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Citations in the corpus

Homotopy theory of modules over operads in symmetric spectra (2007, background): “See also the original article of May [30]; other accounts include Berger and Moerdijk [2], Fresse [8], Ginzburg and Kapranov [11], Hinich [17], Markl, Shnider and Stasheff [29], McClure and Smith [32] and Spitzweck [41].”
The blob complex (2010, background): “TODO: Various citations we might want to make: • [8] McClure and Smith’s review article • [7] May, (inter alia, definition of E∞ operad) • [1, 2] Boardman and Vogt • [4] definition of framed little-discs operad We now turn to establishing the gluing formula for blob homology, restated from Property ”
On the cyclic Deligne conjecture (2004, background): “on the Hochschild cochain complex of a unital, associative algebrawith invariant inner product. This question has been aﬃrmatively answered by Kaufmann, McClure and Smith, Tamarkin; see [6], [9], and [11]. In this note, we give an explicit action of chains of cyclic Sullivan chord diagrams on the re”
Operads and knot spaces (2004, background): “It sends a contraction of edges of T to the collection of contractions on the corresponding edges for trees over P ( T ).”