Free Loop Space Homology of Highly Connected Manifolds

2015/02/11 by Alexander Berglund, Berglund, Alexander, Kaj Börjeson +1
Mathematics · #16E40 #16S37 Secondary: 55P35 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary: 55P50 #math.AT #msc:16E40 #msc:16S37 #msc:55P35 #msc:55P50

paper · pdf · doi:10.48550/arxiv.1502.03356

35 pages

arxiv created 2015/02/11 · arxiv updated 2015/02/12

Abstract

We calculate the homology of the free loop space of (n-1)-connected closed manifolds of dimension at most 3n-2 (n > 1), with the Chas-Sullivan loop product and loop bracket. Over a field of characteristic zero, we obtain an expression for the BV-operator. We also give explicit formulas for the Betti numbers, showing they grow exponentially. Our main tool is the connection between formality, coformality and Koszul algebras that was elucidated in earlier work by the first author.

Related

• The Free Loop Space Homology of (n-1)-connected 2n-manifolds
• Koszul A-infinity algebras and free loop space homology
• Free loop space and homology
• A Homotopy Theoretic Proof of the BV Identity in Loop Homology
• Topological coHochschild Homology and the Homology of Free Loop Spaces