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Vanishing of universal characteristic classes for handlebody groups and boundary bundles

Jeff Giansiracusa, Ulrike Tillmann, Jeffrey Giansiracusa Orcid Logo

Springer/TCMS, Volume: 6, Issue: 1, Pages: 103 - 112

Swansea University Author: Jeffrey Giansiracusa Orcid Logo

Abstract

Using certain Thom spectra appearing in the study of cobordism categories, we show that the odd half of the Miller-Morita-Mumford classes on the mappping class group of a surface with negative Euler characteristic vanish in integral cohomology when restricted to the handlebody subgroup. This is a sp...

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Published in: Springer/TCMS
Published: 2011
URI: https://cronfa.swan.ac.uk/Record/cronfa8377
first_indexed 2013-07-23T12:00:56Z
last_indexed 2018-02-09T04:37:21Z
id cronfa8377
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spelling 2011-10-01T00:00:00.0000000 v2 8377 2012-02-22 Vanishing of universal characteristic classes for handlebody groups and boundary bundles 03c4f93e1b94af60eb0c18c892b0c1d9 0000-0003-4252-0058 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 2012-02-22 MACS Using certain Thom spectra appearing in the study of cobordism categories, we show that the odd half of the Miller-Morita-Mumford classes on the mappping class group of a surface with negative Euler characteristic vanish in integral cohomology when restricted to the handlebody subgroup. This is a special case of a more general theorem valid in all dimensions: universal characteristic classes made from monomials in the Pontrjagin classes (and even powers of the Euler class) vanish when pulled back from BDiff(\partial W) to BDiff(W). Journal Article Springer/TCMS 6 1 103 112 31 12 2011 2011-12-31 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2011-10-01T00:00:00.0000000 2012-02-22T13:37:15.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jeff Giansiracusa 1 Ulrike Tillmann 2 Jeffrey Giansiracusa 0000-0003-4252-0058 3
title Vanishing of universal characteristic classes for handlebody groups and boundary bundles
spellingShingle Vanishing of universal characteristic classes for handlebody groups and boundary bundles
Jeffrey Giansiracusa
title_short Vanishing of universal characteristic classes for handlebody groups and boundary bundles
title_full Vanishing of universal characteristic classes for handlebody groups and boundary bundles
title_fullStr Vanishing of universal characteristic classes for handlebody groups and boundary bundles
title_full_unstemmed Vanishing of universal characteristic classes for handlebody groups and boundary bundles
title_sort Vanishing of universal characteristic classes for handlebody groups and boundary bundles
author_id_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9
author_id_fullname_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9_***_Jeffrey Giansiracusa
author Jeffrey Giansiracusa
author2 Jeff Giansiracusa
Ulrike Tillmann
Jeffrey Giansiracusa
format Journal article
container_title Springer/TCMS
container_volume 6
container_issue 1
container_start_page 103
publishDate 2011
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 0
active_str 0
description Using certain Thom spectra appearing in the study of cobordism categories, we show that the odd half of the Miller-Morita-Mumford classes on the mappping class group of a surface with negative Euler characteristic vanish in integral cohomology when restricted to the handlebody subgroup. This is a special case of a more general theorem valid in all dimensions: universal characteristic classes made from monomials in the Pontrjagin classes (and even powers of the Euler class) vanish when pulled back from BDiff(\partial W) to BDiff(W).
published_date 2011-12-31T03:16:31Z
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score 11.089572

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