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  • "Teorie homotopicky invariantních struktur v topologii byla rozvinuta M Boardmanem a R. Vogtem v roce 1973. První systematický pokus vytvořit analogickou teorii pro algebraické struktury byl učiněn mnohem později, v roce 1999 v žadatelově článku ""Homotopy algebras are homotopy algebras"". Metody tohoto článku byly již úspěšně aplikovány např. v Kontsevičově důkazu Delingeovy doměnky. Konkrétní cíle tohoto projektu jsou (1) formulovat a dokázat ideální homologické perturbační lemma pro komplexy s netriviální algebraickou strukturou, (2) dokázat, že silně homotopické algebry tvoří kategorii, a (3) studovat homotopie morfizmů silně homotopických algeber. Posledním cílem bude (4) položit základy teorie rezolvent PROPů popisujících různé typy bialgeber." (cs)
  • "The theory of homotopy invariant structures in topology was developed by M. Boardman and R. Vogt in 1973. The first systematic attempt to build up a similar theory for algebraic structures was made much later, in 1999 by the applicant in his paper ""Homotopy algebras are homotopy algebras"". Some of the methods of the paper have already been succefully applied, for example, in Kontsevich's proof of Deligne s conjecture. Concrete scientific aims of this project are (1) to formulate and prove an idealhomological perturbation lemma for chain complexes with nontrivial algebraic structure, (2) to prove that strongly homotopy algebras from a category and (3) to study homotopies between morphisms of strongly homotopy algebras. The last aim is (4) to outline a theory of resolutions of PROP s describing various types of bialgebras." (en)
Title
  • Homotopicky invariantní struktury v algebře (cs)
  • Homotopy invariant structures in algebra (en)
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  • algebra; topology; mathematical physics; homological perturbation theory; strongly homotopy algebras (en)
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