Algebra/Topology seminar

Speaker: Johan Alm (Stockholm University)

Title: A universal A-infinity structure on BV algebras

Abstract: The operad of framed little disks is known to be formal, i.e., its 
associated operad of chains is quasi-isomorphic to the its associated 
operad of homology groups. However, the natural morphism from the operad 
of little intervals to the operad of framed little disks, embedding the 
intervals as disks centred on the real axis (with a fixed framing), is 
not formal. It follows that this topologically almost tautological 
morphism should correspond, via formality of the framed little disks, to 
some nontrivial morphism from the A-infinity operad to the homology 
operad of the framed little disks. We give an explicit construction of 
this morphism. The construction is based on the geometry of the moduli 
space of genus zero curves and can be informally regarded as a kind of 
generating function for multiple zeta values. It conjecturally also 
gives a new presentation of the Grothendieck-Teichmueller Lie algebra.