arXiv subjects

Jamil Mortada

Publications and source records attributed to Jamil Mortada.

2 recordsLinked to original sources

arXiv2012

Subgroups of Mod(S) generated by X in {(T_aT_b)^k,(T_bT_a)^k} and Y in {T_a,T_b}

Suppose a and b are distinct isotopy classes of essential simple closed curves in an orientable surface S. Let T_a and T_b represent the respective Dehn twists along a and b. In this paper, we study the subgroups of Mod(S) generated by X and Y, where X belongs to {(T_aT_b)^k,(T_bT_a)^k}, k an integer, and Y belongs to {T_a,T_b}. For a large class of examples, we show that the subgroups and are isomorphic. Moreover, we prove that = whenever i(a,b) = 1 and k is not a multiple of three or i(a,b) bigger or equal to two and k equals plus or minus one. Further, we compute the index in when is a proper subgroup.

math.GT↗

arXiv2011

Artin Relations in the Mapping Class Group

For every integer l bigger than one, we find elements x and y in the mapping class group of an appropriate orientable surface S, satisfying the Artin relation of length l. That is, xyx... = yxy..., where each side of the equality contains l terms. By direct computations, we first find elements x and y in Mod(S) satisfying Artin relations of every even length bigger than 6, and every odd length bigger than 1. Then using the theory of Artin groups, we give two more alternative ways for finding Artin relations in Mod(S). The first provides Artin relations of every length greater than 3, while the second produces Artin relations of every even length greater than 4.

math.GT↗