Algebraic structures on generalized strings
| dc.creator | Chernov, Vladimir | |
| dc.creator | Rudyak, Yuli. B. | |
| dc.date | 2003-06-08 | |
| dc.date.accessioned | 2026-07-07T04:58:41Z | |
| dc.date.available | 2026-07-07T04:58:41Z | |
| dc.description | 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 $\pr(\li α_1\bullet \li α_2)= [α_1, α_2]$ for all $α_1, α_2 \in \bor_*(\NN)$. If $P$ is a boundary, then $\pr \circ \li=0$ and thus $Δ^2=0$ for $Δ=\li \circ \pr$. We show that under certain conditions the operations $Δ$ 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. | |
| dc.description | 9 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0306140 | |
| dc.identifier | http://arxiv.org/abs/math/0306140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67736 | |
| dc.subject | Geometric Topology | |
| dc.subject | Quantum Algebra | |
| dc.subject | 55N22, 55N45, 57R19, 57R45, 17B62, 17B63, 17B81 | |
| dc.title | Algebraic structures on generalized strings | |
| dc.type | text |