Operad-theory-Impact-factor
By modeling computational trees within the algebra, operads generalize the various associative properties already observed in algebras and coalgebras such as Lie algebras or Poisson algebras. Operational equipped sets are omnipresent in mathematics, and many familiar operations share key properties. This proposal addresses problems of topology, in the field of fundamental mathematics. The general purpose of our project is to develop applications of operads (an algebraic device) for the definition of invariants associated with links, manifolds, and stratified spaces. The addition of real numbers, function composition, and string concatenation, are all associative operations with an identity element. Rather than working directly with particular examples of sets and operations, abstracting their common properties and instead of working with algebraic structures is often more convenient. The operads of small discs (and the equivalent operads of small cubes) were introduced in topology for the recognition of iterated loop spaces, in the works of Boardman – Vogt, and May. For an account of these applications, we refer to the paper in the Handbook of algebraic topology. We also refer to the literature for the general definition of an operad in a category and for the accurate definition of the operads of the small discs.
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