|Name||J. Scott Carter|
|Affiliation||University of South Alabama|
|Time||Jan 12 11:10~12:00|
|Title||n-dimensional foams and cocycles that are associated to G-families of quandles|
In this talk, I will introduce the idea of an n-dimensional foam which generalizes trivalent graphs, and the usual notion of a surface foam. Such foams can be knotted in $(n+2)$-dimensional space. Local pictures for the crossing points are obtained in all dimensions. There are different crossing types that are easy to parametrize. Also local crossings have signs associated to them. In all dimensions it is possible to examine quandle colorings and group-flows on $n$-foams. As a result, group-families of quandles, and cocycles that are associated to these can be used to distinguish different knotted foams. The subject of this talk is being developed in conjunction with Masahico Saito.