Bolza Surface
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Bolza surface is a compact Riemann surface of genus 2 with the highest possible order of the conformal automorphism group in this genus, namely 48.The Bolza surface is a (2,3,8) triangle surface. More specifically, the Fuchsian group defining the Bolza surface is a subgroup of the group generated by reflections in the sides of a hyperbolic triangle with angles More specifically, it is a subgroup of the index-two subgroup of the group of reflections...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Bolza surface is a compact Riemann surface of genus 2 with the highest possible order of the conformal automorphism group in this genus, namely 48.The Bolza surface is a (2,3,8) triangle surface. More specifically, the Fuchsian group defining the Bolza surface is a subgroup of the group generated by reflections in the sides of a hyperbolic triangle with angles More specifically, it is a subgroup of the index-two subgroup of the group of reflections, which consists of products of an even number of reflections, which has an abstract presentation in terms of generators s2,s3,s8 and relations s22 = s33 = s88 = 1 as well as s2s3 = s8. The Fuchsian group defining the Bolza surface is also a subgroup of the (3,3,4) triangle group, which is a subgroup of index 2 in the (2,3,8) triangle group. It is interesting to note that the (2,3,8) group does not have a realisation in terms of a quaternion algebra, but the (3,3,4) group does.
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