• Corpus ID: 118641294

Foliated Cobordism and Motion

  title={Foliated Cobordism and Motion},
  author={David Henry Delphenich},
  journal={arXiv: General Relativity and Quantum Cosmology},
  • D. Delphenich
  • Published 24 September 2002
  • Mathematics
  • arXiv: General Relativity and Quantum Cosmology
The mathematical notion of foliated cobordism is presented, and its relationship to both the motion of extended particles and wave motion is detailed. The fact that wave motion, when represented in such a manner on a four-dimensional spacetime, leads to a reduction of the bundle of linear frames to an SO(2)-principle bundle is demonstrated. Invariants of foliated cobordism are discussed as they relate to the aforementioned cases of motion. 
Complex geometry and pre-metric electromagnetism
The intimate link between complex geometry and the problem of the pre-metric formulation of electromagnetism is explored. In particular, the relationship between 3+1 decompositions of R4 and the
Spacetime G-structures I: Topological Defects
The notion of G-structure is defined and various geometrical and topological aspects of such structures are discussed. A particular chain of subgroups in the affine group for Minkowski space is
On the axioms of topological electromagnetism
The axioms of topological electromagnetism that were given by Hehl, Obukhov, and Rubilar are refined by the use of geometrical and topological notions that are found on orientable manifolds. The
The Geometric Origin of the Madelung Potential
Madelung's hydrodynamical forms of the Schrodinger equation and the Klein-Gordon equation are presented. The physical nature of the quantum potential is explored. It is demonstrated that the
Spacetime G-structures II: geometry of the ground states
This article is a continuation of a previous work that dealt with the topological obstructions to the reductions of the bundle of linear frames on a spacetime manifold for a particular chain of


Topology change and monopole creation.
  • Sorkin
  • Mathematics
    Physical review. D, Particles and fields
  • 1986
It is shown that the condition for a topological cobordism to admit an appropriate metric is different in even and odd dimensions, which means that pair creation of Kaluza-Klein monopoles cannot occur via the mechanism considered.
Topological methods in hydrodynamics
A group theoretical approach to hydrodynamics considers hydrodynamics to be the differential geometry of diffeomorphism groups. The principle of least action implies that the motion of a fluid is
Topology in general relativity
A number of theorems and definitions which are useful in the global analysis of relativistic world models are presented. It is shown in particular that, under certain conditions, changes in the
Geometry of Foliations
1 Examples and Definition of Foliations.- 2 Foliations of Codimension One.- 3 Holonomy, Second Fundamental Form, Mean Curvature.- 4 Basic Forms, Spectral Sequence, Characteristic Form.- 5 Transversal
The Hamilton-Cartan formalism in the calculus of variations
In this paper, we give an exposition of the geometry of the calculus of variations in several variables. The main emphasis is on the Hamiltonian formalism via the use of a linear differential form
Spatially integrable space-times
The topological and geometrical restrictions on spatially integrable space-times foliated by space-like hypersurfaces are investigated.
Calculus of variations and partial differential equations of the first order
Continuous convergence, implicit functions, ordinary differential equations Fields of curves and multidimensional surfaces, complete systems Partial differential equations of the first order, theory
Topics on space-time geometry
Several topics in the geometry of space-times are discussed, including the time and space-distributions of the space-time and a geometrical definition of singularities.
Exterior Differential Systems
Basic theorems Cartan-Khler theory linear differential systems the characteristic variety prolongation theory applications of commutative algebra and algebraic geometry to the study of exterior