ROOTS OF DEHN TWISTS ABOUT MULTICURVES
Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 555-583
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A multicurve ${\mathcal{C}}$ in a closed orientable surface Sg of genus g is defined to be a finite collection of disjoint non-isotopic essential simple closed curves. A left-handed Dehn twist $t_{\mathcal{C}}$ about ${\mathcal{C}}$ is the product of left-handed Dehn twists about the individual curves in ${\mathcal{C}}$. In this paper, we derive necessary and sufficient conditions for the existence of a root of $t_{\mathcal{C}}$ in the mapping class group Mod(Sg). Using these conditions, we obtain combinatorial data that correspond to roots, and use it to determine upper bounds on the degree of a root. As an application of our theory, we classify all such roots up to conjugacy in Mod(S4). Finally, we establish that no such root can lie in the level m congruence subgroup of Mod(Sg), for m ≥ 3.
RAJEEVSARATHY, KASHYAP; VAIDYANATHAN, PRAHLAD. ROOTS OF DEHN TWISTS ABOUT MULTICURVES. Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 555-583. doi: 10.1017/S0017089517000283
@article{10_1017_S0017089517000283,
author = {RAJEEVSARATHY, KASHYAP and VAIDYANATHAN, PRAHLAD},
title = {ROOTS {OF} {DEHN} {TWISTS} {ABOUT} {MULTICURVES}},
journal = {Glasgow mathematical journal},
pages = {555--583},
year = {2018},
volume = {60},
number = {3},
doi = {10.1017/S0017089517000283},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000283/}
}
TY - JOUR AU - RAJEEVSARATHY, KASHYAP AU - VAIDYANATHAN, PRAHLAD TI - ROOTS OF DEHN TWISTS ABOUT MULTICURVES JO - Glasgow mathematical journal PY - 2018 SP - 555 EP - 583 VL - 60 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000283/ DO - 10.1017/S0017089517000283 ID - 10_1017_S0017089517000283 ER -
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