arXiv Open Access 2018

Geodesics in the mapping class group

Kasra Rafi Yvon Verberne

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Abstrak

We construct explicit examples of geodesics in the mapping class group and show that the shadow of a geodesic in mapping class group to the curve graph does not have to be a quasi-geodesic. We also show that the quasi-axis of a pseudo-Anosov element of the mapping class group may not have the strong contractibility property. Specifically, we show that, after choosing a generating set carefully, one can find a pseudo-Anosov homeomorphism f, a sequence of points w_k and a sequence of radii r_k so that the ball B(w_k, r_k) is disjoint from a quasi-axis a of f, but for any projection map from mapping class group to a, the diameter of the image of B(w_k, r_k) grows like log(r_k).

Topik & Kata Kunci

math.GR math.GT

Penulis (2)

Kasra Rafi

Yvon Verberne

Format Sitasi

APA MLA BibTeX

Rafi, K., Verberne, Y. (2018). Geodesics in the mapping class group. https://arxiv.org/abs/1810.12489

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Informasi Jurnal

Tahun Terbit: 2018
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓