Tangent bundles and gauge groups

M. Rahula^a, V. Balan<sup>b

a</sup> Faculty of Mathematics and Computer Science, University of Tartu, Tartu, Estonia
^b Faculty of Applied Sciences, University Politehnica of Bucharest, Bucharest, Romania

Abstract: The differentials $T^ka$ $(k\ge1)$ of a diffeomorphism $a$ of a smooth manifold $M$ induce in the fibers of the fiber bundles $T^kM,$ i.e., in the corresponding tangent spaces, linear transformations, which embody the action of the gauge group $\mathcal G_k$. This action extends in a natural way to the osculating subbundles $\mathrm{Osc}^{k-1}M\subset T^kM$.

Keywords: diffeomorphism of a smooth manifold, fiber bundles, action of the gauge group.

UDC: 514.763.2

Received: 17.12.2010

Language: English