TRIANGLE GEOMETRY/TOPOLOGY SEMINAR

      SECOND ANNOUNCEMENT

DATE:               Friday, September 3, 2004            

LOCATION:     Hempfield High School, Room 213 (directions attached)                

                           followed by dinner at “Symposium,” 125 S. Centerville Road, Lancaster.

4:30 TALK:       Ron Umble, Millersville University

               "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 à 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

  Elizabethtown College, Franklin & Marshall College and Millersville University.