On 2-Dimensional Holonomy

نویسندگان

  • João Faria Martins
  • Roger Picken
چکیده

We define the fundamental strict categorical group P2(M, ∗) of a based smooth manifold (M, ∗) and construct categorical holonomies, being smooth morphisms P2(M, ∗) → C(G), where C(G) is a Lie categorical group, by using a notion of categorical connections, which we define. As a result, we are able to define Wilson spheres in this context.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An eight–dimensional approach to G2 manifolds

We develop a systematic approach to G2 holonomy manifolds with an SU(2)× SU(2) isometry using maximal eight-dimensional gauged supergravity to describe D6-branes wrapped on deformed three-spheres. A quite general metric ansatz that generalizes the celebrated Bryant–Salamon metric involves nine functions. We show that only six of them are the independent ones and derive the general first order s...

متن کامل

ar X iv : 0 70 9 . 24 40 v 2 [ he p - th ] 1 5 Fe b 20 08 Time - Dependent Multi - Centre Solutions from New Metrics with Holonomy Sim

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, Sim(n− 2). Ricci-flat metrics with Sim(2) holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a non-zero cosmological constant was exhibited by ...

متن کامل

Time-dependent Multi-centre Solutions from New Metrics with Holonomy Sim(n − 2)

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n− 2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a non-zero cosmological constant was exhibited by ...

متن کامل

D - Brane Probes of Special Holonomy Manifolds , and Dynamics of N = 1 Three - Dimensional Gauge Theories

Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G2 and Spin(7) holonomy. We derive mirror pairs of N = 1 supersymmetric three-dimensional gauge theories, and apply this technique to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of the D2-brane world-volume theory. We derive a “G2 quotient construction” of non-compa...

متن کامل

Finsler manifolds with non-Riemannian holonomy

The aim of this paper is to show that holonomy properties of Finsler manifolds can be very different from those of Riemannian manifolds. We prove that the holonomy group of a positive definite non-Riemannian Finsler manifold of non-zero constant curvature with dimension > 2 cannot be a compact Lie group. Hence this holonomy group does not occur as the holonomy group of any Riemannian manifold. ...

متن کامل

Towards a classification of Lorentzian holonomy groups

If the holonomy representation of an (n + 2)–dimensional simply-connected Lorentzian manifold (M,h) admits a degenerate invariant subspace its holonomy group is contained in the parabolic group (R×SO(n))⋉R. The main ingredient of such a holonomy group is the SO(n)–projection G := prSO(n)(Holp(M,h)) and one may ask whether it has to be a Riemannian holonomy group. In this paper we show that this...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008