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Brackets in the Pontryagin algebras of manifolds. (Crochets dans les algèbres de Pontryagin des variétés.) (English. French summary) Zbl 1416.17012

Given a smooth oriented manifold M with non empty boundary, this book considers the Pontryagin algebras of manifolds with boundary and constructs a bracket in the associated representation algebras. In the first chapter, the authors define representation algebras and recall important facts about brackets and bibrackets. Chapter 2 deals with bibrackets in unital algebras and in categories. In chapter 3, the authors introduce the face homology and reformulate face homology of the path spaces of manifolds in terms of smooth polychains. Chapter 4 is the study of the operations on polychains. Transversality of polychains is investigated and intersection operations in the homology of path spaces are defined. Ih the two last chapters, the authors construct the intersection bibrackets and study its properties in details.

MSC:

17B63 Poisson algebras
55N33 Intersection homology and cohomology in algebraic topology
55P50 String topology
57R19 Algebraic topology on manifolds and differential topology
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