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$A(\infty)$-algebra structure in the cohomology and cohomologies of a free loop space
T. V. Kadeishviliab a A. Razmadze Mathematical Institute, Georgian Academy of Sciences
b Tbilisi Ivane Javakhishvili State University
Abstract:
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, morphism, $A(\infty)$-algebra, cohomology algebra, cohomology module, loop space.
Citation:
T. V. Kadeishvili, “$A(\infty)$-algebra structure in the cohomology and cohomologies of a free loop space”, Algebra, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 177, VINITI, Moscow, 2020, 87–96
Linking options:
https://www.mathnet.ru/eng/into602 https://www.mathnet.ru/eng/into/v177/p87
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Abstract page: | 250 | Full-text PDF : | 80 | References: | 31 |
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