J. Scott Carter
A Survey of Quandle Ideas.
Thu, 02/25/2010 - 16:01 — SomNambulAuthors: J. Scott Carter
Subjects: Geometric Topology
AbstractThis article surveys many aspects of the theory of quandles which
algebraically encode the Reidemeister moves. In addition to knot theory,
quandles have found applications in other areas which are only mentioned in
passing here. The main purpose is to give a short introduction to the subject
and a guide to the applications that have been found thus far for quandle
cocycle invariants.Algebraic Structures Derived from Foams.
Thu, 01/07/2010 - 16:01 — SomNambulAuthors: J. Scott Carter, Masahico Saito
Subjects: Geometric Topology
AbstractFoams are surfaces with branch lines at which three sheets merge. They have
been used in the categorification of sl(3) quantum knot invariants and also in
physics. The 2D-TQFT of surfaces, on the other hand, is classified by means of
commutative Frobenius algebras, where saddle points correspond to
multiplication and comultiplication. In this paper, we explore algebraic
operations that branch lines derive under TQFT. In particular, we investigate
Lie bracket and bialgebra structures.Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces.
Wed, 08/19/2009 - 19:30 — SomNambulAuthors: J. Scott Carter, Kanako Oshiro, Masahico Saito
Subjects: Geometric Topology
AbstractQuandles with involutions that satisfy certain conditions, called good
involutions, can be used to color non-orientable surface-knots. We use
subgroups of signed permutation matrices to construct non-trivial good
involutions on extensions of odd order dihedral quandles.For the smallest example of order 6 that is an extension of the three-element
dihedral quandle, various symmetric quandle homology groups are computed, and
applications to the minimal triple point number of surface-knots are given.
User login
