Bordism invariants of the mapping class group
We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this filtration are the well-known Torelli group and Johnson subgroup...
Main Author: | |
---|---|
Other Authors: | |
Format: | Others |
Language: | English |
Published: |
2009
|
Subjects: | |
Online Access: | http://hdl.handle.net/1911/18635 |
id |
ndltd-RICE-oai-scholarship.rice.edu-1911-18635 |
---|---|
record_format |
oai_dc |
spelling |
ndltd-RICE-oai-scholarship.rice.edu-1911-186352013-10-23T04:13:36ZBordism invariants of the mapping class groupHeap, AaronMathematicsWe define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this filtration are the well-known Torelli group and Johnson subgroup, respectively. We introduce a new representation in terms of spin bordism, and we prove that this single representation contains all of the information given by the Johnson homomorphisms, the Birman-Craggs homomorphisms, and the Morita homomorphisms.Cochran, Tim D.2009-06-04T08:25:15Z2009-06-04T08:25:15Z2004ThesisText70 p.application/pdfhttp://hdl.handle.net/1911/18635eng |
collection |
NDLTD |
language |
English |
format |
Others
|
sources |
NDLTD |
topic |
Mathematics |
spellingShingle |
Mathematics Heap, Aaron Bordism invariants of the mapping class group |
description |
We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this filtration are the well-known Torelli group and Johnson subgroup, respectively. We introduce a new representation in terms of spin bordism, and we prove that this single representation contains all of the information given by the Johnson homomorphisms, the Birman-Craggs homomorphisms, and the Morita homomorphisms. |
author2 |
Cochran, Tim D. |
author_facet |
Cochran, Tim D. Heap, Aaron |
author |
Heap, Aaron |
author_sort |
Heap, Aaron |
title |
Bordism invariants of the mapping class group |
title_short |
Bordism invariants of the mapping class group |
title_full |
Bordism invariants of the mapping class group |
title_fullStr |
Bordism invariants of the mapping class group |
title_full_unstemmed |
Bordism invariants of the mapping class group |
title_sort |
bordism invariants of the mapping class group |
publishDate |
2009 |
url |
http://hdl.handle.net/1911/18635 |
work_keys_str_mv |
AT heapaaron bordisminvariantsofthemappingclassgroup |
_version_ |
1716610962647154688 |