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Articles 1 - 8 of 8

Full-Text Articles in Geometry and Topology

Review: The Relationships Among Multiplicities Of A J-Self-Adjoint Differential Operator's Eigenvalue, Stephan Ramon Garcia Mar 2014

Review: The Relationships Among Multiplicities Of A J-Self-Adjoint Differential Operator's Eigenvalue, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.


Topological Symmetry Groups Of Graphs In 3-Manifolds, Erica Flapan, Harry Tamvakis Jan 2013

Topological Symmetry Groups Of Graphs In 3-Manifolds, Erica Flapan, Harry Tamvakis

Pomona Faculty Publications and Research

We prove that for every closed, connected, orientable, irreducible 3-manifold there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group G there is an embedding T of some graph in a hyperbolic rational homology 3-sphere such that the topological symmetry group of T is isomorphic to G.


Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Erica Flapan, Blake Mellor, Ramin Naimi Jan 2011

Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Erica Flapan, Blake Mellor, Ramin Naimi

Pomona Faculty Publications and Research

We determine for which m the complete graph Km has an embedding in S3 whose topological symmetry group is isomorphic to one of the polyhedral groupsA4, A5 or S4.


Intrinsic Linking And Knotting Are Arbitrarily Complex, Erica Flapan, Blake Mellor, Ramin Naimi Jan 2008

Intrinsic Linking And Knotting Are Arbitrarily Complex, Erica Flapan, Blake Mellor, Ramin Naimi

Pomona Faculty Publications and Research

We show that, given any n and alpha, any embedding of any sufficiently large complete graph in R3 contains an oriented link with components Q1,...,Qn such that for every i not equal to j, Ilk(Qi,Qj)I greater than or equal to alpha and la2(Qi)l greater than or equal to alpha, where a2(Qi) denotes the second coefficient of the Conway polynomial of Qi.


A Model Of Dna Knotting And Linking, Erica Flapan, Dorothy Buck Jan 2007

A Model Of Dna Knotting And Linking, Erica Flapan, Dorothy Buck

Pomona Faculty Publications and Research

We present a model of how DNA knots and links are formed as a result of a single recombination event, or multiple rounds of (processive) recombination events, starting with an unknotted, unlinked, or a (2,m)-torus knot or link substrate. Given these substrates, according to our model all DNA products of a single recombination event or processive recombination fall into a single family of knots and links.


Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor Jan 2006

Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor

Pomona Faculty Publications and Research

We prove that a graph is intrinsically linked in an arbitrary 3–manifold M if and only if it is intrinsically linked in S3. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S3.


Inner Matrices And Darlington Synthesis, Stephan Ramon Garcia Jan 2005

Inner Matrices And Darlington Synthesis, Stephan Ramon Garcia

Pomona Faculty Publications and Research

We describe and parameterize the solutions of the scalar valued Darlington synthesis problem. In the case of rational data we derive a simple procedure for producing all possible solutions.


Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan Jan 2002

Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan

Pomona Faculty Publications and Research

We show that for every m∈N, there exists an n∈N such that every embedding of the complete graph Kn in R3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r∈N such that every embedding of Kr in R3 contains a knot Q with |a2(Q)| ≥ m, where a2(Q) denotes the second coefficient of the Conway polynomial of Q.