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<p>We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principal fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the isomorphism between the semisimple inverse monoid algebra and a matrix algebra which lies at the heart of monoid structure and representation theory. An example that we study in detail is the Ivanov-Kerov monoid of partial permutations. We review motivations from string theory for the resulting grand canonical theory of covers with boundaries.</p>

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Inverse monoid topological quantum field theories and open-closed grand canonical symmetric orbifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月10日

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  • Jan Troost

摘要

We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principal fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the isomorphism between the semisimple inverse monoid algebra and a matrix algebra which lies at the heart of monoid structure and representation theory. An example that we study in detail is the Ivanov-Kerov monoid of partial permutations. We review motivations from string theory for the resulting grand canonical theory of covers with boundaries.