RATIONAL HOMOTOPY THEORY (Graduate Texts in Mathematics 205) By YVES FÉLIX, STEPHEN HALPERIN and JEAN-CLAUDE THOMAS: 535 pp., £41.00, ISBN 0-387-95068-0 (Springer, New York, 2001)

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Toric Topology (2012, background): “Following [112], APL(X) is defined as A (S•X), where S•(X) denotes the total singular complex of X and A : sset→ cdgaQ is the polynomial de Rham functor of [39].”
Compact corigid objects in triangulated categories and co-t-structures (2007, background): “Simply connected cochain DGAs arise naturally in algebraic topology as the cochain algebras of simply connected CW-complexes, see [9] and [17], for example.”
Batalin-Vilkovisky algebra structures on Hochschild Cohomology (2007, unknown): “…by Theorem 22 depends course on the algebra S ∗ ( M ) but also on a fundamental BULLETIN DE LA SOCIÉTÉ MATHÉMATIQUE DE FRANCE class [ m ] ∈ HH − d ( S The Batalin-Vilkovisky Corollary 20, depends of diﬀer-ential forms A PL ( M ) [10], – and of the fundamental class [ M ∈ H d ( A PL ( M ) ∨ ) .”