Points and Curves in the Monster Tower is popular PDF and ePub book, written by Richard Montgomery in 2010-01-15, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Points and Curves in the Monster Tower can be Read Online from any device for your convenience.
Points and Curves in the Monster Tower Book PDF Summary
Cartan introduced the method of prolongation which can be applied either to manifolds with distributions (Pfaffian systems) or integral curves to these distributions. Repeated application of prolongation to the plane endowed with its tangent bundle yields the Monster tower, a sequence of manifolds, each a circle bundle over the previous one, each endowed with a rank $2$ distribution. In an earlier paper (2001), the authors proved that the problem of classifying points in the Monster tower up to symmetry is the same as the problem of classifying Goursat distribution flags up to local diffeomorphism. The first level of the Monster tower is a three-dimensional contact manifold and its integral curves are Legendrian curves. The philosophy driving the current work is that all questions regarding the Monster tower (and hence regarding Goursat distribution germs) can be reduced to problems regarding Legendrian curve singularities.
Detail Book of Points and Curves in the Monster Tower PDF
- Author : Richard Montgomery
- Release : 15 January 2010
- Publisher : American Mathematical Soc.
- ISBN : 9780821848180
- Genre : Mathematics
- Total Page : 154 pages
- Language : English
- PDF File Size : 16,9 Mb
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