A generating set for the palindromic Torelli group
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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Let Tn be the kernel of the natural map Out(Fn) → GLn(Z). We use combinatorial Morse theory to prove that Tn has an Eilenberg–MacLane space which is (2n − 4)-dimensional and that H2n−4(Tn, Z) is not finitely generated (n ≥ 3). In particular, this recovers the result of Krstić–McCool that T3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that Tn is finitely gener...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2015
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2015.15.3535