Pseudo-Anosov map with n-prong singularity - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T17:54:02Z http://mathoverflow.net/feeds/question/109592 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109592/pseudo-anosov-map-with-n-prong-singularity Pseudo-Anosov map with n-prong singularity Bin Yu 2012-10-14T09:27:23Z 2012-10-14T11:23:39Z <p>Whether the following statemant is correct (I guess the answer is "Yes" and I guess that maybe it is trivial for an expert about Pseudo-Anosov map)? </p> <p>"For a given $n\in N$, there exists a closed orientbale surface $\Sigma^n$ such that there exists a pseudo-Anosov diffeomorphism $f_n$ on $\Sigma^n$ with an $n$-prong singularity. "</p> <p>Could you pleae provide me some references or comments? Thank you.</p> http://mathoverflow.net/questions/109592/pseudo-anosov-map-with-n-prong-singularity/109601#109601 Answer by Matheus for Pseudo-Anosov map with n-prong singularity Matheus 2012-10-14T11:23:39Z 2012-10-14T11:23:39Z <p>The answer to your question is yes and essentially the only restriction on the singularity type (=number of prongs) is the one coming from Euler-Poincare formula. For further details, I think an useful reference is, e.g., the book "A Primer on Mapping Class Groups" by B. Farb and D. Margalit (http://press.princeton.edu/titles/9495.html).</p>