2007/07/29 by Tian Yang, Yang, Tian
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT
paper · pdf · doi:10.48550/arxiv.0707.4213
openalex publication_date 2007/07/29 · arxiv created 2010/04/22 · arxiv updated 2010/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result of this paper is to calculate the Batalin-Vilkovisky structure of HH^*(C^*(KPn;R);C^*(KPn;R)) for K=ℂ and ℍ, and R=ℤ and any field; and shows that in the special case when M=ℂP1=S2, and R=ℤ, this structure can not be identified with the BV-structure of ℍ_*(LS2;ℤ) computed by Luc Memichi in \citemenichi2. However, the induced Gerstenhaber structures are still identified in this case. Moreover, according to a recent work of Y.Felix and J.Thomas \citefelix--thomas, the main result of the present paper eventually calculates the BV-structure of the rational loop homology, ℍ_*(LℂPn;ℚ) and ℍ_*(LℍPn;ℚ), of projective spaces.