most recent 30 from http://mathoverflow.net 2013-06-19T05:09:32Z http://mathoverflow.net/feeds/user/7325 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/32198/textbook-or-lecture-notes-in-topological-k-theory Martin Pinsonnault 2010-07-16T16:09:10Z 2011-09-12T17:53:22Z

<p>I am looking for a good introductory level textbook (or set of lecture notes) on classical topological K-Theory that would be suitable for a one-semester graduate course. Ideally, it would require minimal background: standard introductory courses in algebraic topology and differential geometry, would cover core topics (Bott periodicity, Chern character, representation rings, etc) mostly in a self-contained way, and would give interesting examples and exercises. </p> <p>As I learned the subject from multiple books and papers, I don't know a "canonical" reference that gives a coherent picture of the subject. Any suggestions ?</p>

http://mathoverflow.net/questions/30938/diffeomorphism-groups-of-orbifolds Martin Pinsonnault 2010-07-07T19:01:27Z 2010-07-07T20:39:51Z

<p>A lot is known about geometric and topological properties of diffeomorphism groups of surfaces (here, I am mainly thinking about the work of Smale and Eells-Elworthy). Is there anything known for orbisurfaces ? My first guess would be that many of these groups must have contractible components since singular points impose extra conditions somewhat similar to fixed points. Is there a good reference on this topic ?</p>

http://mathoverflow.net/questions/30926/structure-of-kahler-cone/30936#30936 Martin Pinsonnault 2010-07-07T18:45:07Z 2010-07-07T18:45:07Z

<p>To Hirzebruch surfaces, you can add $\mathrm{CP}^2$, its $k$-folds blow-ups, $1\leq k\leq 8$, and some irrational ruled surfaces.</p> <p>Related to this question is the determination of the symplectic cone. This is now understood for rational $4$-manifolds, ruled $4$-manifolds and their blow-ups, and also for some elliptic fibrations.</p> <p>There is a nice survey by Tian-Jun Li of the relations between symplectic and Kahler cones for $4$-manifolds (and complex surfaces). See arXiv:0805.2931.</p>

http://mathoverflow.net/questions/19530/what-is-meant-by-smooth-orbifold/30897#30897 Martin Pinsonnault 2010-07-07T14:37:23Z 2010-07-07T14:37:23Z

<p>There is also a diffeological definition of orbifolds which is often useful in concrete geometric problems, see the paper of Iglesias, Karshon, and Zadka:</p> <p>arXiv:math/0501093</p> <p>or</p> <p><a href="http://www.ams.org/journals/tran/2010-362-06/S0002-9947-10-05006-3/home.html" rel="nofollow">http://www.ams.org/journals/tran/2010-362-06/S0002-9947-10-05006-3/home.html</a></p>

http://mathoverflow.net/questions/30480/particle-physics-and-representations-of-groups/30565#30565 Martin Pinsonnault 2010-07-04T22:39:44Z 2010-07-05T00:22:34Z

<p>There is an excellent introduction by John Baez and John Huerta to the Standard Model and Lie groups theory in the Bulletin of the AMS, vol 47, no. 3, July 2010. In particular, it gives plenty of references and historical notes.</p> <p>I just noticed that this is the same article as the one suggested by Bruce, sorry!</p>

http://mathoverflow.net/questions/32198/textbook-or-lecture-notes-in-topological-k-theory/32209#32209 Martin Pinsonnault 2010-07-18T14:46:04Z 2010-07-18T14:46:04Z

Thanks. I will let you know if I find any typos.

http://mathoverflow.net/questions/32198/textbook-or-lecture-notes-in-topological-k-theory/32203#32203 Martin Pinsonnault 2010-07-18T13:52:40Z 2010-07-18T13:52:40Z

Thanks. I did not know that book and, indeed, it covers a lot of what I need.

http://mathoverflow.net/questions/30938/diffeomorphism-groups-of-orbifolds/30941#30941 Martin Pinsonnault 2010-07-07T19:58:31Z 2010-07-07T19:58:31Z

Well, my question was badly formulated. Here's a second try: Do you know any results on the homotopy type of diffeomorphism groups of non-hyperbolic orbisurfaces (&#224; la Smale), regardless of the techniques used ?

http://mathoverflow.net/questions/30938/diffeomorphism-groups-of-orbifolds/30941#30941 Martin Pinsonnault 2010-07-07T19:51:21Z 2010-07-07T19:51:21Z

Thanks for this quick and illuminating answer. Do you know if some of those results extend to non-hyperbolic orbifolds ?