K. Gongopadhyay, M. M. Mishra, D. Tiwari, “On generalized Jørgensen inequality in <nobr>$\mathrm{SL}(2, \mathbb{C})$</nobr>”, Sib. Èlektron. Mat. Izv., 2019, Volume 16,Pages <nobr>542

Geometry and topology

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

K. Gongopadhyay^a, M. M. Mishra^b, D. Tiwari^c

^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.

UDC: 515.124.2

MSC: 30L99, 53C23, 54D10

Received September 17, 2018, published April 19, 2019

Language: English

DOI: 10.33048/semi.2019.16.035