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Articles 1 - 15 of 15
Full-Text Articles in Geometry and Topology
Wallpaper Groups, Cassondra Fett
Wallpaper Groups, Cassondra Fett
Honors Capstones
Capstone submitted as a graduation requirement for the BSU Honors Program.
Neutrosophic Methods In General Relativity, Florentin Smarandache, Dmitri Rabounski, Larissa Borissova
Neutrosophic Methods In General Relativity, Florentin Smarandache, Dmitri Rabounski, Larissa Borissova
Branch Mathematics and Statistics Faculty and Staff Publications
In this work the authors apply concepts of Neutrosophic Logic to the General Theory of Relativity to obtain a generalisation of Einstein’s fourdimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed. Fundamental features of Neutrosophic Logic are its denial of the Law of Excluded Middle, and open (or estimated) levels of truth, falsity and indeterminancy. Both Neutrosophic Logic and Smarandache Geometry were invented some years ago by one of the authors (F. Smarandache). The application of these purely mathematical theories to General Relativity reveals hitherto unknown …
A Constructive Proof Of Ky Fan's Generalization Of Tucker's Lemma, Timothy Prescott '02, Francis E. Su
A Constructive Proof Of Ky Fan's Generalization Of Tucker's Lemma, Timothy Prescott '02, Francis E. Su
All HMC Faculty Publications and Research
We present a proof of Ky Fan's combinatorial lemma on labellings of triangulated spheres that differs from earlier proofs in that it is constructive. We slightly generalize the hypotheses of Fan's lemma to allow for triangulations of Sn that contain a flag of hemispheres. As a consequence, we can obtain a constructive proof of Tucker's lemma that holds for a more general class of triangulations than the usual version.
Differentials In The Homological Homotopy Fixed Point Spectral Sequence, Robert R. Bruner, John Rognes
Differentials In The Homological Homotopy Fixed Point Spectral Sequence, Robert R. Bruner, John Rognes
Mathematics Faculty Research Publications
We analyze in homological terms the homotopy fixed point spectrum of a T–equivariant commutative S–algebra R. There is a homological homotopy fixed point spectral sequence with E^2_(s,t) = H^(−s)_(gp) (��;H_t(R;��_p)), converging conditionally to the continuous homology H^c_(s+t)(R^(h��);��_p) of the homotopy fixed point spectrum. We show that there are Dyer–Lashof operations β^ϵQ^i acting on this algebra spectral sequence, and that its differentials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the E^(2r)–term of the spectral sequence there are 2r other classes in the E^(2r)–term (obtained mostly by Dyer–Lashof operations …
Orthogonal Curvilinear Coordinates, Lindsey J. Bromenshenkel
Orthogonal Curvilinear Coordinates, Lindsey J. Bromenshenkel
Honors Capstones
Capstone submitted as a graduation requirement for the BSU Honors Program.
Lower Bounds For Simplicial Covers And Triangulations Of Cubes, Adam Bliss '03, Francis E. Su
Lower Bounds For Simplicial Covers And Triangulations Of Cubes, Adam Bliss '03, Francis E. Su
All HMC Faculty Publications and Research
We show that the size of a minimal simplicial cover of a polytope P is a lower bound for the size of a minimal triangulation of P, including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an analysis of the number of exterior faces that a simplex in the cube can have of a specified dimension and volume, and a characterization of corner simplices in terms of their …
A Topological Representation Theorem For Oriented Matroids, Jürgen Bokowski, Simon King, Sussane Mock, Ileana Streinu
A Topological Representation Theorem For Oriented Matroids, Jürgen Bokowski, Simon King, Sussane Mock, Ileana Streinu
Computer Science: Faculty Publications
We present a new direct proof of a topological representation theorem for oriented matroids in the general rank case. Our proof is based on an earlier rank 3 version. It uses hyperline sequences and the generalized Schönflies theorem. As an application, we show that one can read off oriented matroids from arrangements of embedded spheres of codimension one, even if wild spheres are involved.
Continued Radicals, Jamie Johnson
Continued Radicals, Jamie Johnson
Masters Theses & Specialist Projects
If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the …
Inner Matrices And Darlington Synthesis, Stephan Ramon Garcia
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.
Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz
Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz
Mathematics and Statistics Faculty Publications and Presentations
In this note, we provide a conveniently implementable basis for simplicial Nédélec spaces of any order in any space dimension. The main feature of the basis is that it is expressed solely in terms of the barycentric coordinates of the simplex.
Proper Actions Of Automorphism Groups Of Free Products Of Finite Groups, Craig A. Jensen, Yuqing Chen, Henry H. Glover
Proper Actions Of Automorphism Groups Of Free Products Of Finite Groups, Craig A. Jensen, Yuqing Chen, Henry H. Glover
Mathematics Faculty Publications
If G is a free product of finite groups, let ΣAut1(G) denote all (necessarily symmetric) automorphisms of G that do not permute factors in the free product. We show that a McCullough–Miller and Gutiérrez–Krstić derived (also see Bogley–Krstić) space of pointed trees is an EΣAut1(G)-space for these groups.
The Cohomology Of Right Angled Artin Groups With Group Ring Coefficients, Craig A. Jensen
The Cohomology Of Right Angled Artin Groups With Group Ring Coefficients, Craig A. Jensen
Mathematics Faculty Publications
The cohomology of a right-angled Artin group with group ring coefficients is explicitly presented in terms of the cohomology of its defining flag complex. 2000 Mathematics Subject Classification 20F36 (primary), 57M07 (secondary).
Commensurability Classes Of Twist Knots, Jim Hoste, Patrick D. Shanahan
Commensurability Classes Of Twist Knots, Jim Hoste, Patrick D. Shanahan
Mathematics, Statistics and Data Science Faculty Works
In this paper we prove that if MK is the complement of a non-fibered twist knot K in S3, then MK is not commensurable to a fibered knot complement in a Z/2Z-homology sphere. To prove this result we derive a recursive description of the character variety of twist knots and then prove that a commensurability criterion developed by D. Calegari and N. Dunfield is satisfied for these varieties. In addition, we partially extend our results to a second infinite family of 2-bridge knots.
Derived Categories And The Analytic Approach To General Reciprocity Laws. Part I, Michael Berg
Derived Categories And The Analytic Approach To General Reciprocity Laws. Part I, Michael Berg
Mathematics, Statistics and Data Science Faculty Works
We reformulate Hecke's open problem of 1923, regarding the Fourier-analytic proof of higher reciprocity laws, as a theorem about morphisms involving stratified topological spaces. We achieve this by placing Kubota's formulations of n-Hilbert reciprocity in a new topological context, suited to the introduction of derived categories of sheaf complexes. Subsequently, we begin to investigate conditions on associated sheaves and a derived category of sheaf complexes specifically designed for an attack on Hecke's eighty-year-old challenge.
From Loop Groups To 2-Groups, John C. Baez, Danny Stevenson, Alissa S. Crans, Urs Schreiber
From Loop Groups To 2-Groups, John C. Baez, Danny Stevenson, Alissa S. Crans, Urs Schreiber
Mathematics, Statistics and Data Science Faculty Works
We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism called the "Jacobiator". Similarly, a Lie 2-group is a categorified version of a Lie group. If G is a simply-connected compact simple Lie group, there is a 1-parameter family of Lie 2-algebras g_k each having Lie(G) as its Lie algebra of objects, but with a Jacobiator built from the canonical 3-form on G. There appears to be no Lie 2-group …