We describe a simple geometric construction of the fundamental group of the closed connected orientable surface of genus g (g greater or equal 2) presented in terms of 2g complex Mobius transformations as generators and of one relation among them. Our construction allows us to write the equation of any transformation of the above group. Finally, we give a recurrence formula to obtain all the vertices of the tessellation induced by the above group in the open unit disc endowed by the hyperbolic metric.

Mobius transformations and surface groups / Cavicchioli, Alberto. - In: RIVISTA DI MATEMATICA DELLA UNIVERSITÀ DI PARMA. - ISSN 0035-6298. - STAMPA. - 17:(1991), pp. 7-20.

Mobius transformations and surface groups

CAVICCHIOLI, Alberto
1991

Abstract

We describe a simple geometric construction of the fundamental group of the closed connected orientable surface of genus g (g greater or equal 2) presented in terms of 2g complex Mobius transformations as generators and of one relation among them. Our construction allows us to write the equation of any transformation of the above group. Finally, we give a recurrence formula to obtain all the vertices of the tessellation induced by the above group in the open unit disc endowed by the hyperbolic metric.
17
7
20
Mobius transformations and surface groups / Cavicchioli, Alberto. - In: RIVISTA DI MATEMATICA DELLA UNIVERSITÀ DI PARMA. - ISSN 0035-6298. - STAMPA. - 17:(1991), pp. 7-20.
Cavicchioli, Alberto
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/451039
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