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- W1637444505 abstract "A garland based on a manifold $P$ is a finite set of manifolds homeomorphic to $P$ with some of them glued together at marked points. Fix a manifold $M$ and consider a space $NN$ of all smooth mappings of garlands based on $P$ into $M$. We construct operations $bullet$ and $[-,-]$ on the bordism groups $bor_*(NN)$ that give $bor_*(NN)$ the natural graded commutative assosiative and graded Lie algebra structures. We also construct two auto-homomorphisms $pr$ and $li$ of $bor_*(NN)$ such that $pr(li alpha_1bullet li alpha_2)= [alpha_1, alpha_2]$ for all $alpha_1, alpha_2 in bor_*(NN)$. If $P$ is a boundary, then $pr circ li=0$ and thus $Delta^2=0$ for $Delta=li circ pr$. We show that under certain conditions the operations $Delta$ and $bullet$ give rise to Batalin-Vilkoviski and Gerstenhaber algebra structures on $bor_*(NN)$. In a particular case when $P=S^1$, the algebra $bor_*(NN)$ is related to the string-homology algebra constructed by Chas and Sullivan." @default.
- W1637444505 created "2016-06-24" @default.
- W1637444505 creator A5001820777 @default.
- W1637444505 creator A5086340669 @default.
- W1637444505 date "2003-06-08" @default.
- W1637444505 modified "2023-09-25" @default.
- W1637444505 title "Algebraic structures on generalized strings" @default.
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