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Homotopy algebras are homotopy algebras. (English) Zbl 1067.55011
The concept of homotopy invariant algebraic structures for topological spaces formulated by J. M. Boardman and R. M. Vogt [Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics 347. Berlin-Heidelberg-New York: Springer-Verlag. X, 257 p. DM 22.00; $ 09.10 (1973; Zbl 0285.55012)] is transferred to the algebra of chain complexes. It is shown that a certain concept of strongly homotopy algebra which is broad enough to include both classical examples such a strongly homotopy associative algebras, strongly homotopy associative commutative algebras and more recent concepts arising in quantum field theory is homotopy invariant.

MSC:
55U35 Abstract and axiomatic homotopy theory in algebraic topology
55U15 Chain complexes in algebraic topology
18G55 Nonabelian homotopical algebra (MSC2010)
Citations:
Zbl 0285.55012
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