Topological Monodromy of an Integrable Heisenberg Spin Chain
We investigate topological properties of a completely integrable system on S²×S²×S² which was recently shown to have a Lagrangian fiber diffeomorphic to RP³ not displaceable by a Hamiltonian isotopy [Oakley J., Ph.D. Thesis, University of Georgia, 2014]. This system can be viewed as integrating the...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147133 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Topological Monodromy of an Integrable Heisenberg Spin Chain / J. Lane // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862741908404568064 |
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| author | Lane, J. |
| author_facet | Lane, J. |
| citation_txt | Topological Monodromy of an Integrable Heisenberg Spin Chain / J. Lane // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We investigate topological properties of a completely integrable system on S²×S²×S² which was recently shown to have a Lagrangian fiber diffeomorphic to RP³ not displaceable by a Hamiltonian isotopy [Oakley J., Ph.D. Thesis, University of Georgia, 2014]. This system can be viewed as integrating the determinant, or alternatively, as integrating a classical Heisenberg spin chain. We show that the system has non-trivial topological monodromy and relate this to the geometric interpretation of its integrals.
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| first_indexed | 2025-12-07T20:22:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147133 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:22:41Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lane, J. 2019-02-13T17:18:47Z 2019-02-13T17:18:47Z 2015 Topological Monodromy of an Integrable Heisenberg Spin Chain / J. Lane // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J35; 53D12 DOI:10.3842/SIGMA.2015.062 https://nasplib.isofts.kiev.ua/handle/123456789/147133 We investigate topological properties of a completely integrable system on S²×S²×S² which was recently shown to have a Lagrangian fiber diffeomorphic to RP³ not displaceable by a Hamiltonian isotopy [Oakley J., Ph.D. Thesis, University of Georgia, 2014]. This system can be viewed as integrating the determinant, or alternatively, as integrating a classical Heisenberg spin chain. We show that the system has non-trivial topological monodromy and relate this to the geometric interpretation of its integrals. This paper is a contribution to the Special Issue on Algebraic Methods in Dynamical Systems. The full
 collection is available at http://www.emis.de/journals/SIGMA/AMDS2014.html.
 The author would like to thank his advisor Yael Karshon for her guidance and support and
 Leonid Polterovich for suggesting the study of integrable spin chains. Special thanks also goes
 to Joel Oakley for discussing his recent work on displaceability, Anton Izosimov for explaining
 his results on non-degenerate singularities, Peter Crooks for his editorial assistance, and the
 referees for their detailed feedback. The author was supported by NSERC PGS-D and OGS
 scholarships during the preparation of this work. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Topological Monodromy of an Integrable Heisenberg Spin Chain Article published earlier |
| spellingShingle | Topological Monodromy of an Integrable Heisenberg Spin Chain Lane, J. |
| title | Topological Monodromy of an Integrable Heisenberg Spin Chain |
| title_full | Topological Monodromy of an Integrable Heisenberg Spin Chain |
| title_fullStr | Topological Monodromy of an Integrable Heisenberg Spin Chain |
| title_full_unstemmed | Topological Monodromy of an Integrable Heisenberg Spin Chain |
| title_short | Topological Monodromy of an Integrable Heisenberg Spin Chain |
| title_sort | topological monodromy of an integrable heisenberg spin chain |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147133 |
| work_keys_str_mv | AT lanej topologicalmonodromyofanintegrableheisenbergspinchain |