Pomona College

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19942026

most citedA glimpse of the end of the dark ages: the gamma-ray burst of 23 April 2009 at redshift 8.3

625 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

collaborating institutions

Showing math.GTShow all

29 papers · 1 filter

math.GT2024

Topological Symmetry Groups of the Generalized Petersen Graphs

A. Álvarez, E. Flapan, M. Hunnell +5

The topological symmetry group $TSG (Γ)$ of an embedding $Γ$ of a graph in $S^{3}$ is the subgroup of the automorphism group of the graph which is induced by homeomorphisms o…

math.GT2022

Bounds in simple hexagonal lattice and classification of 11-stick knots

Yueheng Bao, Ari Benveniste, Marion Campisi +4

The stick number and the edge length of a knot type in the simple hexagonal lattice (sh-lattice) are the minimal numbers of sticks and edges required, respectively, to construct a…

math.GT2020

Weakly linked embeddings of pairs of complete graphs in $R^{3}$

James Di, Erica Flapan, Spencer Johnson +2

Let $G$ and $H$ be disjoint embeddings of complete graphs $K_{m}$ and $K_{n}$ in $R^{3}$ such that some cycle in $G$ links a cycle in $H$ with non-zero linking number. We say th…

math.GT2020★ 1 cited

Reidemeister Moves in Gauss Diagrams

Sandy Ganzell, Ellen Lehet, Cristina Lopez +2

We provide a simple algorithm for recognizing and performing Reidemeister moves in a Gauss diagram.

math.GT2019

Symmetries of Spatial Graphs in $3$ -manifolds

Erica Flapan, Song Yu

We consider when automorphisms of a graph can be induced by homeomorphisms of embeddings of the graph in a $3$ -manifold. In particular, we prove that every automorphism of a graph…

math.GT2017★ 2 cited

Boltzmann Enhancements of Biquasile Counting Invariants

WonHyuk Choi, Deanna Needell, Sam Nelson

In this paper, we build on the biquasiles and dual graph diagrams introduced in arXiv:1610.06969. We introduce \textit{biquasile Boltzmann weights} that enhance the previous knot c…

math.GT2016

Recent Developments in Spatial Graph Theory

Erica Flapan, Thomas Mattman, Blake Mellor +2

This article presents a survey of some recent results in the theory of spatial graphs. In particular, we highlight results related to intrinsic knotting and linking and results abo…

math.GT2015

Linking number and writhe in random linear embeddings of graphs

Erica Flapan, Kenji Kozai

In order to model entanglements of polymers in a confined region, we consider the linking numbers and writhes of cycles in random linear embeddings of complete graphs in a cube. Ou…

math.GT2013★ 5 cited

Reduced Wu and Generalized Simon Invariants for Spatial Graphs

Erica Flapan, Will Fletcher, Ryo Nikkuni

We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain l…

math.GT2013

Topological Symmetry Groups of Möbius Ladders

Erica Flapan, Emille Davie Lawrence

We classify all groups which can occur as the orientation preserving topological symmetry group of some embedding of a Möbius ladder graph in $S^{3}$ .

math.GT2013

Intrinsic Chirality of Multipartite Graphs

Erica Flapan, Will Fletcher

We classify which complete multipartite graphs are intrinsically chiral.

math.GT2012★ 2 cited

Topological Symmetry Groups for Small Complete Graphs

Dwayne Chambers, Erica Flapan

For each $n \leq 6$ , we characterize all the groups which can occur as either the orientation preserving topological symmetry group or the topological symmetry group of some embeddi…

math.GT2011

Full Subcomplexes of CAT(0) Simplicial Complexes

Rena M. H. Levitt

In this article, I prove that full subcomplexes of CAT(0) simplicial 3-complexes inherit the non positive curvature condition, and describe a family of counterexamples that prove t…

math.GT2011★ 1 cited

Enhancements of the rack counting invariant via N-reduced dynamical cocycles

Alissa S. Crans, Sam Nelson, Aparna Sarkar

We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We pr…

math.GT2011★ 1 cited

Topological Symmetry Groups of Graphs in 3-Manifolds

Erica Flapan, Harry Tamvakis

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 embedd…

math.GT2011

Birack shadow modules and their link invariants

Sam Nelson, Katie Pelland

We introduce an associative algebra Z[X,S] associated to a birack shadow and define enhancements of the birack counting invariant for classical knots and links via representations…

math.GT2010★ 10 cited

Spatial Graphs with Local Knots

Erica Flapan, Blake Mellor, Ramin Naimi

It is shown that for any locally knotted edge of a 3-connected graph in $S^{3}$ , there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setw…

math.GT2010★ 21 cited

Complete graphs whose topological symmetry groups are polyhedral

Erica Flapan, Blake Mellor, Ramin Naimi

We determine for which $m$ , the complete graph $K_{m}$ has an embedding in $S^{3}$ whose topological symmetry group is isomorphic to one of the polyhedral groups: $A_{4}$ , $A_{5}$ , or $S_4…

math.GT2009

Every graph has an embedding in $S^{3}$ containing no non-hyperbolic knot

Erica Flapan, Hugh Howards

In contrast with knots, whose properties depend only on their extrinsic topology in $S^{3}$ , there is a rich interplay between the intrinsic structure of a graph and the extrinsic to…

math.GT2008

Intrinsically triple-linked graphs in RP^3

Joel Foisy, Jared Federman, Kristin McNamara +1

Flapan--Naimi--Pommersheim showed that every spatial embedding of $K_{10}$ , the complete graph on ten vertices, contains a non-split three-component link; that is, $K_{10}$ is intr…

math.GT2008★ 3 cited

Intrinsically Linked Graphs in Projective Space

Joel Foisy, Jason Bustamante, Jared Federman +5

We examine graphs that contain a non-trivial link in every embedding into real projective space, using a weaker notion of unlink than was used by Flapan, et al. We call such graphs…

math.GT2008★ 7 cited

The 2-generalized knot group determines the knot

Sam Nelson, Walter D. Neumann

Generalized knot groups $G_{n} (K)$ were introduced independently by Kelly (1991) and Wada (1992). We prove that $G_{2} (K)$ determines the unoriented knot type and sketch a proof of the…

math.GT2007★ 7 cited

Sampling Lissajous and Fourier knots

Adam Boocher, Jay Daigle, Jim Hoste +1

A Lissajous knot is one that can be parameterized by a single cosine function in each coordinate. Lissajous knots are highly symmetric, and for this reason, not all knots are Lissa…

math.GT2007★ 21 cited

A Topological Characterization Of Knots and Links Arising From Site-Specific Recombination

Dorothy Buck, Erica Flapan

We develop a topological model of knots and links arising from a single (or multiple processive) round(s) of recombination starting with an unknot, unlink, or (2,m)-torus knot or l…