Related papers: Bowling ball representation of virtual string link…
For a weak 2-group, we construct a bicategory of flat 2-group bundles over differentiable stacks as a localization of a functor bicategory. This description is amenable to explicit geometric constructions. For example, we show that flat…
We introduce the notion of the space of parallel strings with partially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to construct a machinery…
We enhance the quandle counting invariants of oriented classical and virtual knots and links using a construction similar to quandle modules but inspired by symplectic quandle operations rather than Alexander quandle operations. Given a…
In this paper, we introduce biquandle power brackets, an infinite family of invariants of oriented links containing the classical skein invariants and the quandle and biquandle 2-cocycle invariants as special cases. Biquandle power brackets…
Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…
An analytic model of long string network evolution, recently developed by the authors, is presented in detail, and modified to describe string loop evolution. By treating the average string velocity, as well as the characteristic…
We consider vacuum tunneling of a new kind where the false vacua are not translationally invariant, but have topological defects that break some of their translational symmetries. In the particular case where the topological defects are…
Equations which define classical configurations of strings in $R^3$ are presented in a simple form. General properties as well as particular classes of solutions of these equations are considered.
This talk deals with the old problem of formulatingn a covariant quantum theory of superstrings, ``covariant'' here meaning having manifest Lorentz symmetry and supersymmetry. The advantages and disadvantages of several quantization methods…
Multicrossings, which have previously been defined for classical knots and links, are extended to virtual knots and links. In particular, petal diagrams are shown to exist for all virtual knots.
A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of…
We develop the study of the twelve intersection polynomials of long virtual knots, previously introduced in our preceding paper. We define two geometric invariants, the $1$- and $2$-supporting genera, using two distinct surface…
This talk is divided into two parts. The first part reviews some of the duality relationships between superstring theories. These relationships are interpreted as providing evidence for the existence of a unique underlying fundamental…
We give an elementary introduction to classical and quantum bosonic string theory.
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
It is shown that the string concept results naturally from considerations of gravitation. This paper describes a derivation of linearized general relativity based upon the hypotheses of special covariance and the existence of a…
We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.
We introduce birack brackets, skein invariants of birack-colored framed classical and virtual knots and links with values in a commutative unital ring. The multiset of birack bracket values over the homset from a framed link's fundamental…
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via…
In the present paper we give a new method for converting virtual knots and links to virtual braids. Indeed the braiding method given in this paper is quite general, and applies to all the categories in which braiding can be accomplished. We…