%0 Generic %1 Yang2007 %A Yang, Tian %D 2007 %K batalinvilkovisky cohomology string topology %T A Batalin-Vilkovisky Algebra structure on the Hochschild Cohomology of Truncated Polynomials %U http://arxiv.org/abs/0707.4213 %X The main result of this paper is to calculate the Batalin-Vilkovisky structure of $HH^*(C^*(KP^n;R);C^*(KP^n;R))$ for $ K=C$ and $H$, and $R=Z$ and any field; and shows that in the special case when $M=CP^1=S^2$, and $R=Z$, this structure can not be identified with the BV-structure of $H_*(LS^2;Z)$ computed by Luc Memichi in menichi2. However, the induced Gerstenhaber structures are still identified in this case. Moreover, according to a recent work of Y.Felix and J.Thomas felix--thomas, the main result of the present paper eventually calculates the BV-structure of the rational loop homology, $H_*(LCP^n;Q)$ and $H_*(LHP^n;Q)$, of projective spaces.

@misc{Yang2007, abstract = { The main result of this paper is to calculate the Batalin-Vilkovisky structure of $HH^*(C^*(\mathbf{K}P^n;R);C^*(\mathbf{K}P^n;R))$ for $ \mathbf{K}=\mathbb{C}$ and $\mathbb{H}$, and $R=\mathbb{Z}$ and any field; and shows that in the special case when $M=\mathbb{C}P^1=S^2$, and $R=\mathbb{Z}$, this structure can not be identified with the BV-structure of $\mathbb{H}_*(LS^2;\mathbb{Z})$ computed by Luc Memichi in \cite{menichi2}. However, the induced Gerstenhaber structures are still identified in this case. Moreover, according to a recent work of Y.Felix and J.Thomas \cite{felix--thomas}, the main result of the present paper eventually calculates the BV-structure of the rational loop homology, $\mathbb{H}_*(L\mathbb{C}P^n;\mathbb{Q})$ and $\mathbb{H}_*(L\mathbb{H}P^n;\mathbb{Q})$, of projective spaces. }, added-at = {2010-04-28T20:24:26.000+0200}, author = {Yang, Tian}, biburl = {https://www.bibsonomy.org/bibtex/21026471232f3f956e43541ede8d04684/uludag}, description = {A Batalin-Vilkovisky Algebra structure on the Hochschild Cohomology of Truncated Polynomials}, interhash = {4ddfa6cb549242f7ff6d98497fdaf863}, intrahash = {1026471232f3f956e43541ede8d04684}, keywords = {batalinvilkovisky cohomology string topology}, note = {cite arxiv:0707.4213 }, timestamp = {2010-04-28T20:24:26.000+0200}, title = {A Batalin-Vilkovisky Algebra structure on the Hochschild Cohomology of Truncated Polynomials}, url = {http://arxiv.org/abs/0707.4213}, year = 2007 }