scholarly journals Torelli group, Johnson kernel, and invariants of homology spheres

2020 ◽  
Vol 11 (2) ◽  
pp. 379-410
Author(s):  
Shigeyuki Morita ◽  
Takuya Sakasai ◽  
Masaaki Suzuki
Keyword(s):  
Torelli Group

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

scholarly journals A Birman exact sequence for the Torelli subgroup of Aut(Fn)

2016 ◽  
Vol 26 (03) ◽  
pp. 585-617 ◽  
Author(s):  
Matthew Day ◽  
Andrew Putman
Keyword(s):  
Exact Sequence ◽  
Recent Work ◽  
Homology Group ◽  
Entire Group ◽  
Torelli Group

We develop an analogue of the Birman exact sequence for the Torelli subgroup of [Formula: see text]. This builds on earlier work of the authors, who studied an analogue of the Birman exact sequence for the entire group [Formula: see text]. These results play an important role in the authors’ recent work on the second homology group of the Torelli group.

scholarly journals Generating the Torelli group

2012 ◽  
Vol 58 (1) ◽  
pp. 165-188 ◽  
Author(s):  
Allen Hatcher ◽  
Dan Margalit
Keyword(s):  
Torelli Group

scholarly journals A lower bound of the distortion of the Torelli group in the mapping class group with boundary components

2017 ◽  
Vol 26 (08) ◽  
pp. 1750049
Author(s):  
Erika Kuno ◽  
Genki Omori
Keyword(s):  
Lower Bound ◽  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Oriented Surface

We prove that the Torelli group of an oriented surface with any number of boundary components is at least exponentially distorted in the mapping class group by using Broaddus–Farb–Putman’s techniques. Further we show that the distortion of the Torelli group in the level [Formula: see text] mapping class group is the same as that in the mapping class group.

scholarly journals Towards representation stability for the second homology of the Torelli group

2012 ◽  
Vol 16 (3) ◽  
pp. 1725-1765 ◽  
Author(s):  
Søren K Boldsen ◽  
Mia Hauge Dollerup
Keyword(s):  
Torelli Group ◽  
Representation Stability

scholarly journals Corrigendum: Irreducible decompositon of the Magnus representation of the Torelli group

2004 ◽  
Vol 69 (2) ◽  
pp. 349-349
Author(s):  
Masaaki Suzuki
Keyword(s):  
Torelli Group ◽  
Magnus Representation

Due to a printing error, a significant graph on page 12 was omitted from the paper [1].

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