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Topological Monodromy of an Integrable Heisenberg Spin Chain
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Topological Monodromy of an Integrable Heisenberg Spin Chain
Інший ID:
2010 Mathematics Subject Classification: 37J35; 53D12
DOI:10.3842/SIGMA.2015.062
DOI:10.3842/SIGMA.2015.062
Посилання:
Topological Monodromy of an Integrable Heisenberg Spin Chain / J. Lane // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 22 назв. — англ.
Підтримка:
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.
Дата:
2015
Переглядів:
454
Завантажень:
224
Анотація:
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.
