Quantitative K-Theory Related to Spin Chern Numbers
We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine wh...
Збережено в:
| Дата: | 2014 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146609 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quantitative K-Theory Related to Spin Chern Numbers / T.A. Loring // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146609 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1466092019-02-12T01:24:02Z Quantitative K-Theory Related to Spin Chern Numbers Loring, T.A. We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine which values of the norm of the commutator guarantee that the indices are defined, where they are equal, and what quantitative results on the distance to a pair with a different index are possible. We validate a method of computing spin Chern numbers that was developed with Hastings and only conjectured to be correct. Specifically, the Pfaffian-Bott index can be computed by the ''log method'' for commutator norms up to a specific constant. 2014 Article Quantitative K-Theory Related to Spin Chern Numbers / T.A. Loring // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 19M05; 46L60; 46L80 DOI:10.3842/SIGMA.2014.077 http://dspace.nbuv.gov.ua/handle/123456789/146609 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine which values of the norm of the commutator guarantee that the indices are defined, where they are equal, and what quantitative results on the distance to a pair with a different index are possible. We validate a method of computing spin Chern numbers that was developed with Hastings and only conjectured to be correct. Specifically, the Pfaffian-Bott index can be computed by the ''log method'' for commutator norms up to a specific constant. |
| format |
Article |
| author |
Loring, T.A. |
| spellingShingle |
Loring, T.A. Quantitative K-Theory Related to Spin Chern Numbers Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Loring, T.A. |
| author_sort |
Loring, T.A. |
| title |
Quantitative K-Theory Related to Spin Chern Numbers |
| title_short |
Quantitative K-Theory Related to Spin Chern Numbers |
| title_full |
Quantitative K-Theory Related to Spin Chern Numbers |
| title_fullStr |
Quantitative K-Theory Related to Spin Chern Numbers |
| title_full_unstemmed |
Quantitative K-Theory Related to Spin Chern Numbers |
| title_sort |
quantitative k-theory related to spin chern numbers |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146609 |
| citation_txt |
Quantitative K-Theory Related to Spin Chern Numbers / T.A. Loring // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT loringta quantitativektheoryrelatedtospinchernnumbers |
| first_indexed |
2023-05-20T17:25:12Z |
| last_indexed |
2023-05-20T17:25:12Z |
| _version_ |
1796153253838192640 |