Specific Representations for Members of the Holonomy Group

2000 ◽  
pp. 171-198
Author(s):  
John Snygg
Keyword(s):  
Holonomy Group

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

scholarly journals The eta invariant and equivariant bordism of flat manifolds with cyclic holonomy group of odd prime order

2009 ◽  
Vol 37 (3) ◽  
pp. 275-306 ◽  
Author(s):  
Peter B. Gilkey ◽  
Roberto J. Miatello ◽  
Ricardo A. Podestá
Keyword(s):  
Prime Order ◽  
Holonomy Group ◽  
Eta Invariant ◽  
Flat Manifolds ◽  
Equivariant Bordism

scholarly journals Averaging formula for Nielsen coincidence numbers

2007 ◽  
Vol 186 ◽  
pp. 69-93 ◽  
Author(s):  
Seung Won Kim ◽  
Jong Bum Lee
Keyword(s):  
Normal Subgroup ◽  
Finite Index ◽  
Holonomy Group ◽  
Smooth Manifolds

AbstractIn this paper we study the averaging formula for Nielsen coincidence numbers of pairs of maps (f,g): M→N between closed smooth manifolds of the same dimension. Suppose that G is a normal subgroup of Π = π1(M) with finite index and H is a normal subgroup of Δ = π1(N) with finite index such that Then we investigate the conditions for which the following averaging formula holdswhere is any pair of fixed liftings of (f, g). We prove that the averaging formula holds when M and N are orientable infra-nilmanifolds of the same dimension, and when M = N is a non-orientable infra-nilmanifold with holonomy group ℤ2 and (f, g) admits a pair of liftings on the nil-covering of M.

scholarly journals The Holonomy Group III. Metrisable Spaces

1960 ◽  
Vol 9 (1) ◽  
pp. 89-122
Author(s):  
Vaiclav Hlavaty
Keyword(s):  
Holonomy Group ◽  
Group Iii

scholarly journals On the Holonomy Groups of Linear Connections

1956 ◽  
Vol 10 ◽  
pp. 97-100 ◽  
Author(s):  
Jun-Ichi Hano ◽  
Hideki Ozeki
Keyword(s):  
Linear Group ◽  
Affine Space ◽  
General Linear Group ◽  
Affine Connection ◽  
Holonomy Group ◽  
Linear Connection ◽  
General Linear ◽  
Linear Connections ◽  
Holonomy Groups ◽  
Lie Subgroup

In this note we show in § 1, as the main result, that any connected Lie subgroup of the general linear group GL(n, R) can be realized as the holonomy group of a linear connection, i.e. the homogeneous holonomy group of the associeted affine connection, defined on an affine space of dimension n (n ≧ 2).

scholarly journals Riemann Space with Two-Parametric Homogeneous Holonomy Group

1952 ◽  
Vol 4 ◽  
pp. 35-42
Author(s):  
Minoru Kurita
Keyword(s):  
Alternative Treatment ◽  
Holonomy Group ◽  
Riemann Space ◽  
Group A ◽  
Rotational Part

The rotational part of the holonomy group of a Riemann space is called its homogeneous holonomy group. A Riemann space, whose homogeneous holonomy group is one-parametric, was investigated by Liber and an alternative treatment of the same problem was given by S. Sasaki [1]. I will treat here a Riemann space with two-parametric homogeneous holonomy group and prove the following theorem by the method analogous to that of [1]. I thank Prof. T. Ootuki for his kind advice.

scholarly journals The Holonomy Group I. The Curvature Tensor

1959 ◽  
Vol 8 (2) ◽  
pp. 285-307 ◽  
Author(s):  
Vaiclav Hlavaty
Keyword(s):  
Curvature Tensor ◽  
Holonomy Group ◽  
Group I

Broken chiral symmetries and the holonomy group

1972 ◽  
Vol 11 (2) ◽  
pp. 427-433
Author(s):  
D. V. Volkov
Keyword(s):  
Holonomy Group ◽  
Chiral Symmetries
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