A fundamental domain for the Fermat curves and their quotients (Q2763796)
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scientific article; zbMATH DE number 1693183
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A fundamental domain for the Fermat curves and their quotients |
scientific article; zbMATH DE number 1693183 |
Statements
17 November 2002
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uniformization
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Fermat curve
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singular homology group
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intersection product
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fundamental domain
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quotient curves
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A fundamental domain for the Fermat curves and their quotients (English)
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Let \(F_N: X^N+ Y^N= 1\) be the Fermat curve of \(N\)th degree, with \(N\geq 4\). In this paper the author obtains a basis for the singular homology group \(H_1(F_N,\mathbb{Z})\) and specifies the intersection product in \(H_1(F_N,\mathbb{Z})\). His method is based on the construction of a fundamental domain for \(F_N\) using basic facts from hyperbolic geometry. Furthermore, the same computations are developed for the quotient curves of the Fermat curves of prime exponent.
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