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Articles 1 - 12 of 12
Full-Text Articles in Geometry and Topology
The Fine Structure Of The Kasparov Groups Ii: Topologizing The Uct, Claude Schochet
The Fine Structure Of The Kasparov Groups Ii: Topologizing The Uct, Claude Schochet
Mathematics Faculty Research Publications
The Kasparov Groups KK∗(A,B) have a natural structure as pseudopolonais groups. In this paper we analyze how this topology interacts with the terms of the Universal Coefficient Theorem (UCT) and the splitting sof the UCT constructed by J. Rosenberg and the author, as well as its canonical three term decomposition which exists under bootstrap hypotheses. We show that the various topologies on [cursive]Ext^{1}_{ℤ}(K∗(A),K∗(B)) and other related groups mostly coincide. Then we focus attention on the Milnor sequence and the fine structure subgroup of KK∗(A,B). …
A Polytopal Generalization Of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, Francis E. Su
A Polytopal Generalization Of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, Francis E. Su
All HMC Faculty Publications and Research
We prove the following conjecture of Atanassov (Studia Sci. Math. Hungar.32 (1996), 71–74). Let T be a triangulation of a d-dimensional polytope P with n vertices v1, v2,…,vn. Label the vertices of T by 1,2,…,n in such a way that a vertex of T belonging to the interior of a face F of P can only be labelled by j if vj is on F. Then there are at least n−d full dimensional simplices of T, each labelled with d+1 different labels. We …
Tilings Of Low-Genus Surfaces By Quadrilaterals, John Gregoire, Isabel Averil
Tilings Of Low-Genus Surfaces By Quadrilaterals, John Gregoire, Isabel Averil
Mathematical Sciences Technical Reports (MSTR)
In contribution to the classification of all tilings of low-genus surfaces, the kaleidoscopic and non-kaleidoscopic tilings by quadrilaterals are given up to genus 12. As part of their classification, the algebraic structure of the conformal tiling groups and the geometric structure of the tiles are specified. In addition, several infinite classes of tilings and tiling groups are presented.
Computational Geometry Column 43, Joseph O'Rourke
Computational Geometry Column 43, Joseph O'Rourke
Computer Science: Faculty Publications
The concept of pointed pseudo-triangulations is defined and a few of its applications described.
The Mathematics Of T. Benny Rushing, James Keesling, Luis Montejano, Gerard A. Venema
The Mathematics Of T. Benny Rushing, James Keesling, Luis Montejano, Gerard A. Venema
University Faculty Publications and Creative Works
No abstract provided.
Representing Homology Classes Of Simply Connected 4-Manifolds, Vo Thanh Liem, Gerard A. Venema
Representing Homology Classes Of Simply Connected 4-Manifolds, Vo Thanh Liem, Gerard A. Venema
University Faculty Publications and Creative Works
The main theorem asserts that every 2-dimensional homology class of a compact simply connected PL 4-manifold can be represented by a codimension-0 submanifold consisting of a contractible manifold with a single 2-handle attached. One consequence of the theorem is the fact that every map of S2 into a simply connected, compact PL 4-manifold is homotopic to an embedding if and only if the same is true for every homotopy equivalence. The theorem is also the main ingredient in the proof of the following result: If W is a compact, simply connected, PL submanifold of S4, then each element of H2(W;ℤ) …
Nonorthogonal Polyhedra Built From Rectangles, Melody Donoso, Joseph O'Rourke
Nonorthogonal Polyhedra Built From Rectangles, Melody Donoso, Joseph O'Rourke
Computer Science: Faculty Publications
We prove that any polyhedron of genus zero or genus one built out of rectangular faces must be an orthogonal polyhedron, but that there are nonorthogonal polyhedra of genus seven all of whose faces are rectangles. This leads to a resolution of a question posed by Biedl, Lubiw, and Sun [BLS99].
Enumerating Foldings And Unfoldings Between Polygons And Polytopes, Erik D. Demaine, Martin L. Demaine, Anna Lubiw, Joseph O'Rourke
Enumerating Foldings And Unfoldings Between Polygons And Polytopes, Erik D. Demaine, Martin L. Demaine, Anna Lubiw, Joseph O'Rourke
Computer Science: Faculty Publications
We pose and answer several questions concerning the number of ways to fold a polygon to a polytope, and how many polytopes can be obtained from one polygon; and the analogous questions for unfolding polytopes to polygons. Our answers are, roughly: exponentially many, or nondenumerably infinite.
Applications Of Graph Theory To Separability, Stephen Young
Applications Of Graph Theory To Separability, Stephen Young
Mathematical Sciences Technical Reports (MSTR)
Let S be a surface with a triangular tiling T. Let R be a reflection a side of one of the triangles; so that R is an orientation reversing isometry of the surface. Define M = {s in S |S : Rs = s}. We then say that the surface S separates along the reflection R if S-R has two components. This paper considers the applications of graph theoretic methods to determining whether a reflection is separating or not and compares the algorithmic efficiency of these methods to the current known methods.
Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan
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.
A Density Property Of The Tori And Duality, Peter Loth
A Density Property Of The Tori And Duality, Peter Loth
Mathematics Faculty Publications
In this note, a short proof of a recent theorem of D. Dikranjan and M. Tkachenko is given, and their result is extended.
Vertex-Unfoldings Of Simplicial Manifolds, Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, Joseph O'Rourke
Vertex-Unfoldings Of Simplicial Manifolds, Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, Joseph O'Rourke
Computer Science: Faculty Publications
We present an algorithm to unfold any triangulated 2-manifold (in particular, any simplicial polyhedron) into a non-overlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is connected, but it may have a disconnected interior; the triangles are connected at vertices, but not necessarily joined along edges. We extend our algorithm to establish a similar result for simplicial manifolds of arbitrary dimension.