On Mar 17, 2008, at 3:38 PM, Gary S. Bekkum wrote:

**
Geometric torsions and invariants of manifolds with triangulated
boundary**
(Submitted on 2 Mar 2008)

Abstract: Geometric
torsions are torsions of acyclic complexes of vector spaces which consist of
differentials of geometric quantities assigned to the elements of a manifold
triangulation. We use geometric torsions to construct invariants for a manifold
with a triangulated boundary. These invariants can be naturally united in a
vector, and a change of the boundary triangulation corresponds to a linear
transformation of this vector. Moreover, when two manifolds are glued by their
common boundary, these vectors undergo scalar multiplication, i.e., they work
according to M. Atiyah's axioms for a topological quantum field theory.

http://arxiv.org/abs/0803.0123
**
Elie Cartan's torsion in geometry and in field theory, an
essay**
(Submitted on 9 Nov 2007)

Abstract: We review the
application of torsion in field theory. First we show how the notion of torsion
emerges in differential geometry. In the context of a Cartan circuit, torsion is
related to translations similar as curvature to rotations. Cartan's
investigations started by analyzing Einsteins general relativity theory and by
taking recourse to the theory of Cosserat continua. In these continua, the
points of which carry independent translational and rotational degrees of
freedom, there occur, besides ordinary (force) stresses, additionally spin
moment stresses. In a 3-dimensional continuized crystal with dislocation lines,
a linear connection can be introduced that takes the crystal lattice structure
as a basis for parallelism. Such a continuum has similar properties as a
Cosserat continuum, and the dislocation density is equal to the torsion of this
connection. Subsequently, these ideas are applied to 4-dimensional spacetime. A
translational gauge theory of gravity is displayed (in a Weitzenboeck or
teleparallel spacetime) as well as the viable Einstein-Cartan theory (in a
Riemann-Cartan spacetime). In both theories, the notion of torsion is contained
in an essential way. Cartan's spiral staircase is described as a 3-dimensional
Euclidean model for a space with torsion, and eventually some controversial
points are discussed regarding the meaning of torsion.

http://arxiv.org/abs/0711.1535
**
Einstein's Apple: His First Principle of Equivalence**
(Submitted on 29 Mar 2007)

Abstract: After a
historical discussion of Einstein's 1907 principle of equivalence, a homogeneous
gravitational field in Minkowski spacetime is constructed. It is pointed out
that the reference frames in gravitational theory can be understood as spaces
with a flat connection and torsion defined through teleparallelism. This kind of
torsion was introduced by Einstein in 1928. The concept of torsion is discussed
through simple examples and some historical observations.

http://arxiv.org/abs/gr-qc/0703149
**
Is Torsion a Fundamental Physical Field?**
(Submitted on 5 Feb 2007)

Abstract: The local
Lorentz group is introduced in flat space-time, where the resulting Dirac and
Yang-Mills equations are found, and then generalized to curved space-time: if
matter is neglected, the Lorentz connection is identified with the contortion
field, while, if matter is taken into account, both the Lorentz connection and
the spinor axial current are illustrated to contribute to the torsion of
space-time.

http://arxiv.org/abs/gr-qc/0702024