OPERADS IN ALGEBRA, TOPOLOGY AND PHYSICS (Mathematical Surveys and Monographs 96) By M ARTIN M ARKL , S TEVE S HNIDER and J IM S TASHEFF : 349 pp., US$89.00, ISBN 0-8218-2134-2 (American…

By John C. Baez. 2003

169 citations recorded by the source corpus.

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In Algebra and Number Theory

Citations in the corpus

Homotopy Algebras Inspired by Classical Open-Closed String Field Theory (2004, background): “In particular, a first order solution for c̄ ∈ Hc is preserved to be a first order solution in ↑Coder(T cHo) by an L∞-morphism.”
Homological perturbation theory for algebras over operads (2009, methodology): “To solve this problem, we introduce thick maps of O–algebras and special thick maps that we call pseudo-derivations that serve as appropriate generalizations of algebra homotopies for the purposes of homological perturbation theory.”
A bordism approach to string topology (2003, unknown): “We want to point out that all the constructions performed in this section work with a generalized homology theory h∗ under some mild assumptions ([28]): - the associated cohomology theory h∗ is multiplicative, - h∗ satisfies the infinite wedge axioms.”
On spineless cacti, Deligne's conjecture and Connes-Kreimer's Hopf algebra (2003, background): “In the following trees will play a key role for indexing purposes and in the definition of operads and operadic actions.”
On a theorem of Kontsevich (2002, unknown): “See [7] or [17].”
Arc Operads and Arc Algebras (2002, methodology): “Taking the arc complexes as the basic objects, we construct several operads and suboperads out of them, by specializing the general structure to more restricted ones, thereby controlling the “information carried by the cobordisms”.”
On the operad of associative algebras with derivation (2009, background): “One can consult for instance [14], or [13], for more details.”