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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 542–546 (Mi semr1077)  

Geometry and topology

On generalized Jørgensen inequality in $\mathrm{SL}(2, \mathbb{C})$

K. Gongopadhyaya, M. M. Mishrab, D. Tiwaric

a Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, SAS Nagar, Punjab, 140306, India
b Department of Mathematics, Hansraj College, University of Delhi, Delhi, 110007, India
c Department of Mathematics, University of Delhi, Delhi, 110007, India

Abstract: Wang, Jiang and Cao have obtained a generalized version of the Jørgensen inequality in Proc. Indian Acad. Sci. Math. Sci., 123(2):245–251, 2013, for two generator subgroups of $\mathrm{SL}(2, \mathbb{C})$ where one of the generators is loxodromic. We prove that their inequality is strict.

Keywords: Jørgensen inequality, discreteness.

Funding Agency Grant Number
Science and Engineering Research Board MTR/2017/000355
Gongopadhyay acknowledges partial support from SERB MATRICS grant MTR/2017/000355. Tiwari is supported by NBHM-SRF.


DOI: https://doi.org/10.33048/semi.2019.16.035

Full text: PDF file (126 kB)
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Document Type: Article
UDC: 515.124.2
MSC: 30L99, 53C23, 54D10
Received September 17, 2018, published April 19, 2019
Language: English

Citation: K. Gongopadhyay, M. M. Mishra, D. Tiwari, “On generalized Jørgensen inequality in $\mathrm{SL}(2, \mathbb{C})$”, Sib. Èlektron. Mat. Izv., 16 (2019), 542–546

Citation in format AMSBIB
\Bibitem{GonMisTiw19}
\by K.~Gongopadhyay, M.~M.~Mishra, D.~Tiwari
\paper On generalized J\o{}rgensen inequality in $\mathrm{SL}(2, \mathbb{C})$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 542--546
\mathnet{http://mi.mathnet.ru/semr1077}
\crossref{https://doi.org/10.33048/semi.2019.16.035}


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