Zero Partition CyclesA Recursive Formula for Characteristic Classes of Surface Bundles
Zero Partition Cycles
A Recursive Formula for Characteristic Classes of Surface Bundles
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DissertationDate of Exam
03.02.2017Date of Publication
25.04.2017Advisor
Hamenstädt, UrsulaCo-Referee
Ebert, JohannesMetadata
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Abstract
This thesis is concerned with characteristic classes of surface bundles. A complete description of the ring of stable rational characteristic classes is given by the work of Madsen and Weiss as the polynomial ring in the Miller-Morita-Mumford classes. This work introduces characteristic classes, which are are given by partitions of zeroes of abelian differentials. These classes are not new, but translate the notion of strata of abelian differentials to real-differential surface bundles. The Isomorphism-Theorem 4.4.3 exposes the partition classes as alternative basis for the ring of stable characteristic classes. The proof of the isomorphism theorem is carried out via a recursive computation in terms of the Miller-Morita-Mumford classes.
Classification (DDC)
510 MathematikPedron, Mark: Zero Partition Cycles : A Recursive Formula for Characteristic Classes of Surface Bundles. - Bonn, 2017. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-46573
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-46573
@phdthesis{handle:20.500.11811/7141,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-46573,
author = {{Mark Pedron}},
title = {Zero Partition Cycles : A Recursive Formula for Characteristic Classes of Surface Bundles},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2017,
month = apr,
note = {This thesis is concerned with characteristic classes of surface bundles. A complete description of the ring of stable rational characteristic classes is given by the work of Madsen and Weiss as the polynomial ring in the Miller-Morita-Mumford classes. This work introduces characteristic classes, which are are given by partitions of zeroes of abelian differentials. These classes are not new, but translate the notion of strata of abelian differentials to real-differential surface bundles. The Isomorphism-Theorem 4.4.3 exposes the partition classes as alternative basis for the ring of stable characteristic classes. The proof of the isomorphism theorem is carried out via a recursive computation in terms of the Miller-Morita-Mumford classes.},
url = {https://hdl.handle.net/20.500.11811/7141}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-46573,
author = {{Mark Pedron}},
title = {Zero Partition Cycles : A Recursive Formula for Characteristic Classes of Surface Bundles},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2017,
month = apr,
note = {This thesis is concerned with characteristic classes of surface bundles. A complete description of the ring of stable rational characteristic classes is given by the work of Madsen and Weiss as the polynomial ring in the Miller-Morita-Mumford classes. This work introduces characteristic classes, which are are given by partitions of zeroes of abelian differentials. These classes are not new, but translate the notion of strata of abelian differentials to real-differential surface bundles. The Isomorphism-Theorem 4.4.3 exposes the partition classes as alternative basis for the ring of stable characteristic classes. The proof of the isomorphism theorem is carried out via a recursive computation in terms of the Miller-Morita-Mumford classes.},
url = {https://hdl.handle.net/20.500.11811/7141}
}
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