%0 Generic %1 Dowdall2010 %A Dowdall, Spencer %D 2010 %K dilatation intersection number versus %T Dilatation versus self-intersection number for point-pushing pseudo-Anosov homeomorphisms %U http://arxiv.org/abs/1004.3936 %X A filling curve $\gamma$ on a based surface $S$ determines a pseudo-Anosov homeomorphism $P(\gamma)$ of $S$ via the process of "point-pushing along $\gamma$." We consider the relationship between the self-intersection number $i(\gamma)$ of $\gamma$ and the dilatation of $P(\gamma)$; our main result is that the dilatation is bounded between $(i(\gamma)+1)^1/5$ and $9^i(\gamma)$. We also bound the least dilatation of any pseudo-Anosov in the point-pushing subgroup of a closed surface and prove that this number tends to infinity with genus. Lastly, we investigate the minimal entropy of any pseudo-Anosov homeomorphism obtained by pushing along a curve with self-intersection number $k$ and show that, for a closed surface, this number grows like $łog(k)$.

@misc{Dowdall2010, abstract = { A filling curve $\gamma$ on a based surface $S$ determines a pseudo-Anosov homeomorphism $P(\gamma)$ of $S$ via the process of "point-pushing along $\gamma$." We consider the relationship between the self-intersection number $i(\gamma)$ of $\gamma$ and the dilatation of $P(\gamma)$; our main result is that the dilatation is bounded between $(i(\gamma)+1)^{1/5}$ and $9^{i(\gamma)}$. We also bound the least dilatation of any pseudo-Anosov in the point-pushing subgroup of a closed surface and prove that this number tends to infinity with genus. Lastly, we investigate the minimal entropy of any pseudo-Anosov homeomorphism obtained by pushing along a curve with self-intersection number $k$ and show that, for a closed surface, this number grows like $\log(k)$. }, added-at = {2010-04-28T20:29:23.000+0200}, author = {Dowdall, Spencer}, biburl = {https://www.bibsonomy.org/bibtex/2473053261939fc2384ba6a2e56f939e5/uludag}, description = {Dilatation versus self-intersection number for point-pushing pseudo-Anosov homeomorphisms}, interhash = {d6bdc5f8d0ab9b3b7e64b749d5dd929e}, intrahash = {473053261939fc2384ba6a2e56f939e5}, keywords = {dilatation intersection number versus}, note = {cite arxiv:1004.3936 Comment: 48 pages, 21 figures}, timestamp = {2010-04-28T20:29:23.000+0200}, title = {Dilatation versus self-intersection number for point-pushing pseudo-Anosov homeomorphisms}, url = {http://arxiv.org/abs/1004.3936}, year = 2010 }