Clayton Shonkwiler
Pontryagin invariants and integral formulas for Milnor's triple linking number.
Wed, 01/19/2011 - 16:01 — SomNambulAuthors: Clayton Shonkwiler, David Shea Vela-Vick, Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin
Subjects: Geometric Topology
AbstractTo each three-component link in the 3-sphere, we associate a geometrically
natural characteristic map from the 3-torus to the 2-sphere, and show that the
pairwise linking numbers and Milnor triple linking number that classify the
link up to link homotopy correspond to the Pontryagin invariants that classify
its characteristic map up to homotopy. This can be viewed as a natural
extension of the familiar fact that the linking number of a two-component link
in 3-space is the degree of its associated Gauss map from the 2-torus to the
2-sphere.Legendrian contact homology and nondestabilizability.
Wed, 10/21/2009 - 14:15 — SomNambulAuthors: Clayton Shonkwiler, David Shea Vela-Vick
Subjects: Geometric Topology
AbstractWe provide the first example of a Legendrian knot with nonvanishing contact
homology whose Thurston-Bennequin invariant is not maximal.Legendrian contact homology and nondestabilizability.
Wed, 10/21/2009 - 14:15 — SomNambulAuthors: Clayton Shonkwiler, David Shea Vela-Vick
Subjects: Geometric Topology
AbstractWe provide the first example of a Legendrian knot with nonvanishing contact
homology whose Thurston-Bennequin invariant is not maximal.Poincare duality angles for Riemannian manifolds with boundary.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Clayton Shonkwiler
Subjects: Differential Geometry
AbstractOn a compact Riemannian manifold with boundary, the absolute and relative
cohomology groups appear as certain subspaces of harmonic forms. DeTurck and
Gluck showed that these concrete realizations of the cohomology groups
decompose into orthogonal subspaces corresponding to cohomology coming from the
interior and boundary of the manifold. The principal angles between these
interior subspaces are all acute and are called Poincare duality angles.Poincare duality angles for Riemannian manifolds with boundary.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Clayton Shonkwiler
Subjects: Differential Geometry
AbstractOn a compact Riemannian manifold with boundary, the absolute and relative
cohomology groups appear as certain subspaces of harmonic forms. DeTurck and
Gluck showed that these concrete realizations of the cohomology groups
decompose into orthogonal subspaces corresponding to cohomology coming from the
interior and boundary of the manifold. The principal angles between these
interior subspaces are all acute and are called Poincare duality angles.
User login
