Generalized chillingworth classes on subsurface torelli groups

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2018

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Ünlü Eroğlu, Hatice

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The Torelli group is the subgroup of the mapping class group that acts trivially on homology. Putman's subsurface Torelli groups are an important construction for working with the Torelli group, as they restore the functoriality essential for the inductive arguments on which mapping class group arguments are invariably based. The other important structure on the Torelli group is the Johnson homomorphism. The contraction of the image of the Johnson homomorphism is the Chillingworth class. In this thesis, a combinatorial description of the Chillingworth class is derived for the subsurface Torelli groups. This thesis also brings in the naturality and uniqueness properties on the map whose image is the dual of the Chillingworth classes of the subsurface Torelli groups. Moreover, a relation between the Chillingworth classes of the subsurface Torelli groups and the partitioned Johnson homomorphism is presented.

Subject Keywords

Group theory., Torelli theorem., Homomorphisms (Mathematics).

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http://etd.lib.metu.edu.tr/upload/12622427/index.pdf
https://hdl.handle.net/11511/27749

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

H. Ünlü Eroğlu, “Generalized chillingworth classes on subsurface torelli groups,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.