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Klein foams as families of real forms of Riemann surfaces
Advances in Theoretical and Mathematical Physics. 2017. Vol. 21. No. 1. P. 231-241.
Gusein-Zade S., Natanzon Sergey M.
Klein foams are analogues of Riemann surfaces for surfaces with one-dimensional singularities. They first appeared in mathematical physics (string theory etc.). By definition a Klein foam is constructed from Klein surfaces by gluing segments on their boundaries. We show that, a Klein foam is equivalent to a family of real forms of a complex algebraic curve with some structures. This correspondence reduces investigations of Klein foams to investigations of real forms of Riemann surfaces. We use known properties of real forms of Riemann surfaces to describe some topological and analytic properties of Klein foams.
Keywords: foamsпенаklein surfacesклейновы поверхностиreal foams of Riemann surfacesвещественные формы римановых поверхностей
Publication based on the results of:
Sabir M.Gusein-Zade, Natanzon S., / Cornell University. Series math "arxiv.org". 2015. No. 00047.
Klein foams are analogues of Riemann surfaces for surfaces with one-dimensional singularities. They first appeared in mathematical physics (string theory etc.). By definition a Klein foam is constructed from Klein surfaces by gluing segments on their boundaries. We show that, a Klein foam is equivalent to a family of real forms of a complex algebraic ...
Added: September 22, 2016
Costa A., Gusein-Zade S., Natanzon S. M., Indiana University Mathematics Journal 2011 Vol. 60 No. 3 P. 985-995
Klein foams are analogues of Riemann and Klein surfaces with one-dimensional singularities. We prove that the field of dianalytic functions on a Klein foam Ω coincides with the field of dianalytic functions on a Klein surface K Ω We construct the moduli space of Klein foams, and we prove that the set of classes of ...
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A Klein surface is a generalisation of a Riemann surface to the case of non-orientable surfaces or surfaces with boundary. The category of Klein surfaces is isomorphic to the category of real algebraic curves. An m-spin structure on a Klein surface is a complex line bundle whose m-th tensor power is the cotangent bundle. We ...
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