Related papers: Compactification, topology change and surgery theo…
In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.
Four-dimensional CDT (causal dynamical triangulations) is a lattice theory of geometries which one might use in an attempt to define quantum gravity non-perturbatively, following the standard procedures of lattice field theory. Being a…
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
We study toroidal compactifications of string theories which include compactification of a timelike coordinate. Some new features in the theory of toroidal compactifications arise. Most notably, Narain moduli space does not exist as a…
In these two lectures I describe the difficulties one encounters when trying to construct a framework in which to describe topology change in classical general relativity where one sticks to the assumption of an everywhere non-singular…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
Recently there have been discussions about which complex metrics should be allowable in quantum gravity. These discussions assumed that the matter fields were real valued. We make the observation that for compactified solutions it makes…
We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…
A fully realistic and systematic effective field theory model of a 3-brane universe is constructed. It consists of a six-dimensional gravitating spacetime, containing several, approximately parallel (3+1)-dimensional defects, or…
This paper concerns the quantisation of a rigid body in the framework of ``covariant quantum mechanics'' on a curved spacetime with absolute time. The basic idea is to consider the multi-configuration space, i.e. the configuration space for…
We consider the future causal boundary as a tool to find obstructions to conformal extensions, the latter being a slight generalization to conformal compactifications.
This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients considered here are compact symplectic manifolds (or more generally orbifolds), which arise as the symplectic quotients of a symplectic…
The stabilization of moduli is one of the main problems in string theory. In this talk I will discuss some stringy mechanisms based on non-geometrical compactifications to obtain four dimensional models with a reduced number of moduli.
Compactification can control chaotic Mixmaster behavior in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac-Moody algebras. We show that different compactifications…
In the usual procedure for toroidal Kaluza-Klein reduction, all the higher-dimensional fields are taken to be independent of the coordinates on the internal space. It has recently been observed that a generalisation of this procedure is…
Consider an involution of a smooth projective variety over a field of characteristic not two. We look at the relations between the variety and the fixed locus of the involution from the point of view of cobordism. We show in particular that…
We prove that total spaces of $CP^2$-bundles generate the oriented cobordism ring $\Omega_*$. Combined with the surgery lemma this yields a somewhat different proof of Gromov's and Lawson's theorem that all simply connected non-spin…
We investigate the $\mathcal F$-Borel complexity of topological spaces in their different compactifcations. We provide a simple proof of the fact that a space can have arbitrarily many different complexities in different compactifications.…
We study the ground state wave function for a universe which is topologically a lens space within the Regge calculus approach. By restricting the four dimensional simplicial complex to be a cone over the boundary lens space, described by a…