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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2015
Main Author: Lane, J.
Format: Article
Language:English
Published: Інститут математики НАН України 2015
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147133
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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
id nasplib_isofts_kiev_ua-123456789-147133
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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Topological Monodromy of an Integrable Heisenberg Spin Chain
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Topological Monodromy of an Integrable Heisenberg Spin Chain
spellingShingle Topological Monodromy of an Integrable Heisenberg Spin Chain
Lane, J.
title_short 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_sort topological monodromy of an integrable heisenberg spin chain
author Lane, J.
author_facet Lane, J.
publishDate 2015
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147133
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.
work_keys_str_mv AT lanej topologicalmonodromyofanintegrableheisenbergspinchain
first_indexed 2025-12-07T20:22:41Z
last_indexed 2025-12-07T20:22:41Z
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