A normal generating set for the Torelli group of a compact non-orientable surface
نویسندگان
چکیده
منابع مشابه
Generating the Torelli Group
We give a new proof of the theorem of Birman–Powell that the Torelli subgroup of the mapping class group of a closed orientable surface of genus at least 3 is generated by simple homeomorphisms known as bounding pair maps. The key ingredient is a proof that the subcomplex of the curve complex of the surface spanned by curves within a fixed homology class is connected.
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Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup Ig of the genus g mapping class group has a finite generating set whose size grows cubically with respect to g. Our main tool is a new space called the handle graph on which Ig acts cocompactly.
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2017
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-017-0295-0