TRIANGLE GEOMETRY/TOPOLOGY SEMINAR
SECOND ANNOUNCEMENT
DATE:
LOCATION: Hempfield High
School,
Room 213 (directions attached)
followed by dinner at “Symposium,”
"Some New Cochain Operations on Permutahedra"
ABSTRACT: (Joint
work with Samson Saneblidze.) When U is an algebra,
the S-U
diagonal and “transverse coproduct” on the permutahedra P induce
a pair of
cup products on cellular cochains C^*(P;U). If TH is the module of
free tensors
on a graded module H, the module U=End(TH) is naturally en-
dowed with two external cross products, each giving rise to
a pair of cup pro-
ducts. We use these cup products to bimultiplicatively extend maps in U =
End(TH)
to maps in TTU. This defines a
(non-linear) map d_ : U ŕ TTU,
called
the “biderivative,” that determines the compatibility
relations among the
operations
in an “A_\infty-bialgebra.” Quite remarkably, the homology of a
loop space
carries a canonical A_\infty-bialgebra structure. This gives a rich
and
intricate topological invariant now open for study.
EVERYONE WELCOME
PLEASE FORWARD THIS ANNOUNCEMENT TO ANYONE
INTERESTED
The Triangle Geometry/Topology Seminar is
sponsored jointly by