期刊
JOURNAL OF MATHEMATICAL PHYSICS
卷 58, 期 6, 页码 -出版社
AMER INST PHYSICS
DOI: 10.1063/1.4984309
关键词
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资金
- Polish Ministry of Science and Higher Education [DI2013016543]
- European Research Council [QOLAPS]
- CTP PAS research grant
- Marie Curie International Outgoing Fellowship
We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our approach is based on some fundamental combinatorial properties of the configuration spaces, Mayer-Vietoris sequences for different parts of configuration spaces, and some limited use of discrete Morse theory. As one of the results, we derive the closed-form formulae for ranks of the homology groups for indistinguishable particles on tree graphs. We also give a detailed discussion of the second homology group of the configuration space of both distinguishable and indistinguishable particles. Our motivation is the search for new kinds of quantum statistics. Published by AIP Publishing.
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