Homotopy Algebras are Homotopy Algebras

Details Homotopy Algebras are Homotopy Algebras Homotopy Algebras are Homotopy Algebras

1999-07-22

arxiv.org/abs/math/9907138v3

Mathematics

Algebraic Topology

LaTeX 2.09, 31 pages, article 12pt + bezier, substantially revised

Scientific paper

We prove that strongly homotopy algebras (such as $A_\infty$, $C_\infty$, sh
Lie, $B_\infty$, $G_\infty$,...) are homotopically invariant in the category of
chain complexes. An important consequence is a rigorous proof that `strongly
homotopy structures transfer over chain homotopy equivalences.'

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