Monoids in the fundamental groups of the complement of logarithmic free divisors in C^3

Details Monoids in the fundamental groups of the complement of logarithmic free divisors in C^3 Monoids in the fundamental groups of the complement of logarithmic free divisors in C^3

2009-11-17

arxiv.org/abs/0911.3305v1

Mathematics

Group Theory

28 pages, 4 figures

Scientific paper

We study monoids generated by Zariski-van Kampen generators in the 17 fundamental groups of the complement of logarithmic free divisors in C^3 listed by Sekiguchi (Theorem 1). Five of them are Artin monoids and eight of them are free abelian monoids. The remaining four monoids are not Gaussian and, hence, are neither Garside nor Artin (Theorem 2). However, we introduce, similarly to Artin monoids, fundamental elements and show their existence (Theorem 3). One of the four non-Gaussian monoids satisfies the cancellation condition (Theorem 4).

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