Related papers: Geometry of Calugareanu's theorem
Given a planar oval, consider the maximal area of inscribed $n$-gons resp. the minimal area of circumscribed $n$-gons. One obtains two sequences indexed by $n$, and one of Dowker's theorems states that the first sequence is concave and the…
A major open problem in the theory of twisted commutative algebras (tca's) is proving noetherianity of finitely generated tca's. For bounded tca's this is easy, in the unbounded case, noetherianity is only known for Sym(Sym^2(C^\infty)) and…
We review the algebraic field theory based completely on a nonlinear generalization of the CR complex analiticity conditions to the noncommutative algebra of biquaternions. Any biquaternionic field possesses natural twistor structure and,…
A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group…
We define the notion of a twisted topological graph algebra associated to a topological graph and a $1$-cocycle on its edge set. We prove a stronger version of a Vasselli's result. We expand Katsura's results to study twisted topological…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
The search for a geometrical understanding of dualities in string theory, in particular T-duality, has led to the development of modern T-duality covariant frameworks such as Double Field Theory, whose mathematical structure can be…
We study the fate of discrete gauge groups and discrete charges of gravitational theories under twisted circle compactification. We then apply our results to six-dimensional F-theory vacua with discrete gauge symmetries and relate them to…
Within the framework of a Kaluza-Klein theory, we provide the geometrization of a generic (Abelian and non-Abelian) gauge coupling, which comes out by choosing a suitable matter fields dependence on the extra-coordinates. We start by the…
We consider a planar waveguide with "twisted" boundary conditions. By twisting we mean a special combination of Dirichlet and Neumann boundary conditions. Assuming that the width of the waveguide goes to zero, we identify the effective…
The swing-twist decomposition is a standard routine in motion planning for humanoid limbs. In this paper the decomposition formulas are derived and discussed in terms of Clifford algebra. With the decomposition one can express an arbitrary…
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries…
Ribbons of two-dimensional lattices have properties depending sensitively on the morphology of the two edges. For regular ribbons with two parallel straight edges, the atomic chains terminating the two edges may have more than one choices…
The twist construction is a method to build new interesting examples of geometric structures with torus symmetry from well-known ones. In fact it can be used to construct arbitrary nilmanifolds from tori. In our previous paper, we presented…
A generalization of Wilsonian lattice gauge theory may be obtained by considering the possible self-adjoint extensions of the electric field operator in the Hamiltonian formalism. In the special case of 3D $\mathrm{U}(1)$ gauge theory these…
A detailed version of preprint "Self-linking number of a real algebraic link" by the same author, alg-geom/9410030. For a nonsingular real algebraic curve in 3-dimensional projective space or 3-sphere, a new integer-valued characteristic is…
We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view…
This paper illustrates a computational approach to Culler-Morgan-Shalen theory using ideal triangulations, spun-normal surfaces and tropical geometry. Certain affine algebraic sets associated to the Whitehead link complement as well as…
We begin a coarse geometric study of Hilbert geometry. Actually we give a necessary and sufficient condition for the natural boundary of a Hilbert geometry to be a corona, which is a nice boundary in coarse geometry. In addition, we show…
The regularity of the Rees ring of the edge ideal of a finite simple graph is studied. We show that the matching number is a lower and matching number~$+1$ is an upper bound of the regularity, if the Rees algebra is normal. In general the…