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Metric topology on the moduli space

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Metric topology on the moduli space

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Deng, J. (2021). Metric topology on the moduli space. Applied General Topology. 22(1):11-15. https://doi.org/10.4995/agt.2021.13066

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Título: Metric topology on the moduli space
Autor: Deng, Jialong
Fecha difusión:
Resumen:
[EN] We define the smooth Lipschitz topology on the moduli space and show that each conformal class is dense in the moduli space endowed with Gromov-Hausdorff topology, which offers an answer to Tuschmann’s question.
Palabras clave: Gromov-Hausdorff topology , Ε-topology , Lipschitz-topology , Smooth Lipschitz-topology
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2021.13066
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2021.13066
Agradecimientos:
I thank Xuchao Yao for useful discussions.
Tipo: Artículo

References

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N. A'Campo, L. Ji and A. Papadopoulos, On the early history of moduli and Teichmüller spaces, arXiv e-prints, page arXiv:1602.07208, Feb 2016.

D. Burago, Y. Burago and S. Ivanov, A course in metric geometry, volume 33, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2001. https://doi.org/10.1090/gsm/033

D. A. Edwards, The structure of superspace, in: Studies in topology (Proc. Conf., Univ. North Carolina, Charlotte, N. C., 1974 dedicated to Math. Sect. Polish Acad. Sci.), pages 121-133, 1975. https://doi.org/10.1016/B978-0-12-663450-1.50017-7

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C.-H. Li, Quantum fluctuations, conformal deformations, and Gromov's topology - Wheeler, DeWitt, and Wilson meeting Gromov, arXiv e-prints, page arXiv:1509.03895, Sep 2015.

W. Tuschmann, Spaces and moduli spaces of Riemannian metrics, Front. Math. China 11, no. 5 (2016), 1335-1343. https://doi.org/10.1007/s11464-016-0576-1

W. Tuschmann and D. J. Wraith, Moduli spaces of Riemannian metrics, volume 46, Oberwolfach Seminars, Birkhäuser Verlag, Basel, 2015. https://doi.org/10.1007/978-3-0348-0948-1

J. A. Wheeler, Superspace, in: Analytic methods in mathematical physics (Sympos., Indiana Univ., Bloomington, Ind., 1968), pages 335-378, 1970.

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