most recent 30 from http://mathoverflow.net 2013-05-26T09:36:58Z http://mathoverflow.net/feeds/question/72495 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72495/where-to-start-with-research-regarding-maslov-index-class Tobias 2011-08-09T17:54:32Z 2012-01-04T16:59:20Z

<p>Hi,</p> <p>I am a physicist and currently doing my bachelor thesis about geometric quantization. In the book by Bates and Weinstein I encountered the Maslov index, which seems to be very important :-).</p> <p>But unfortunately my education didn't include anything in the direction of algebra beyond the scope of basic linear algebra. My present research about this topic showed that the Maslov class is an element of the integral cohomology of the manifold. But I couldn't find an introduction or something like this to 'integral cohomology' and I was lost in the big realm of cohomology. (For example: What is the difference of de Rham cohomology, Cech cohomology, Cech - de Rham cohomology and the needed integral cohomogogy). </p> <p>So could someone provide me with a "path" along the topics I have to study to be able to understand Maslov classes. </p> <p>Thanks in advance, Tobias!</p>

http://mathoverflow.net/questions/72495/where-to-start-with-research-regarding-maslov-index-class/72502#72502 Igor Rivin 2011-08-09T18:45:13Z 2011-08-09T18:45:13Z

<p>The early paper by Arnold:</p> <p><a href="http://www.maths.ed.ac.uk/~aar/papers/arnold3.pdf" rel="nofollow">http://www.maths.ed.ac.uk/~aar/papers/arnold3.pdf</a></p> <p>Seems quite lucid (though does talk about cohomologies some -- they might be hard to avoid given the subject matter).</p>

http://mathoverflow.net/questions/72495/where-to-start-with-research-regarding-maslov-index-class/72503#72503 Andrew Ranicki 2011-08-09T18:52:42Z 2011-08-09T18:52:42Z

<p>May I recommend self-study with <a href="http://www.maths.ed.ac.uk/~aar/maslov.htm" rel="nofollow">http://www.maths.ed.ac.uk/~aar/maslov.htm</a> ?</p>

http://mathoverflow.net/questions/72495/where-to-start-with-research-regarding-maslov-index-class/72506#72506 Greg Friedman 2011-08-09T19:12:08Z 2011-08-09T19:12:08Z

<p>This paper outlines several different approaches to the Maslov index: Cappell, Sylvain E.; Lee, Ronnie; Miller, Edward Y. On the Maslov index. Comm. Pure Appl. Math. 47 (1994), no. 2, 121–186. Link <a href="http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160470202/abstract" rel="nofollow">here</a></p> <p>If you're looking for general background on cohomology and coming from a physics background, a good starting point might be Differential Forms in Algebraic Topology by Bott and Tu.</p>

http://mathoverflow.net/questions/72495/where-to-start-with-research-regarding-maslov-index-class/84886#84886 Liviu Nicolaescu 2012-01-04T15:26:07Z 2012-01-04T16:59:20Z

<p>There are different incarnation of the Maslov index. The one that I prefer is the one proposed in Arnold's paper suggested by Igor Rivin. The paper by Cappell-Lee-Miller suggested by Greg Friedman is also an excellent source. (These two papers helped me understand this concept but they addressed primarilty to a mathematical audience.) </p> <p>Maslov introduced his index in his investigation of asymptotics of certain oscillatory appearing in quantization problems. I suspect this is closest to what had in mind. It is sometime known as the Hormander index. Section 3.4 of Duistermaat's book <em>Fourier Integral Operators</em> has a rather efficient description of the Maslov index. As an aside, the operators introduced and investigated by Maslov are special examples of Fourier integral operators.</p>