Type: Article
Publication Date: 2003-12-16
Citations: 7
DOI: https://doi.org/10.1002/mana.200310125
Abstract For connected reductive linear algebraic structure groups it is proven that every web is holonomically isolated. This means that all parallel transports, occurring in a web, may already be obtained by modifying an arbitrary connection in an arbitrarily given neighbourhood of the interior of such a set of paths. Moreover, it is shown that the possible tuples of parallel transports in a web form a Lie subgroup of the corresponding power of the structure group. This Lie subgroup is explicitly calculated and turns out to be independent of the chosen local trivializations. Additionally, explicit necessary and sufficient criteria for the holonomical independence of webs are derived. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)