Mathematics – Algebraic Topology
Scientific paper
2003-09-28
Mathematics
Algebraic Topology
28 pages, revised version, new appendix by Dennis Sullivan added
Scientific paper
We show that the complex $C_\bullet X$ of rational simplicial chains on a compact and triangulated Poincar\'e duality space $X$ of dimension $d$ is an A$_\infty$ coalgebra with $\infty$ duality. This is the structure required for an A$_\infty$ version of the cyclic Deligne conjecture. One corollary is that the shifted Hochschild cohomology $HH^{\bullet+d} (C^\bullet X, C_\bullet X)$ of the cochain algebra $C^\bullet X$ with values in $C_\bullet X$ has a BV structure. This implies, if $X$ is moreover simply connected, that the shifted homology $H_{\bullet+d}LX$ of the free loop space admits a BV structure. An appendix by Dennis Sullivan gives a general local construction of $\infty$ structures.
Sullivan Dennis
Tradler Thomas
Zeinalian Mahmoud
No associations
LandOfFree
Infinity Structure of Poincare Duality Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Infinity Structure of Poincare Duality Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinity Structure of Poincare Duality Spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-370846