Geodesic
$A(\infty)$-algebra structure in the cohomology and cohomologies of a free loop space
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 177 (2020), pp. 87-96

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The cohomology algebra of the space $H^*(X)$ defines neither cohomology modules of the loop space $H^*(\Omega X)$ nor cohomologies of the free loop space $H^*(\Lambda X)$. But by the author's minimality theorem, there exists a structure of $A(\infty)$-algebra $(H^*(X),\{m_i\})$ on $H^*(X)$, which determines $H^*(\Omega X)$. We also show that the same $A(\infty)$-algebra $(H^*(X),\{m_i\})$ determines also cohomology modules $H^*(\Lambda X)$.
Keywords: Hochschild homology, $A(\infty)$-algebra, cohomology algebra, cohomology module, loop space.
Mots-clés : morphism 
@article{INTO_2020_177_a9,
     author = {T. V. Kadeishvili},
     title = {$A(\infty)$-algebra structure in the cohomology and cohomologies of a free loop space},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {87--96},
     publisher = {mathdoc},
     volume = {177},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_177_a9/}
}
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T. V. Kadeishvili. $A(\infty)$-algebra structure in the cohomology and cohomologies of a free loop space. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 177 (2020), pp. 87-96. http://geodesic.mathdoc.fr/item/INTO_2020_177_a9/