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.