Fundamental group for the complement of the Cayley's singularities

M. Amram; M. Dettweiler; M. Friedman; M. Teicher

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arXiv · 0803.3005

Fundamental group for the complement of the Cayley's singularities

M. Amram·M. Dettweiler·M. Friedman·M. Teicher

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Abstract

Given a singular surface X, one can extract information on it by investigating the fundamental group $π_1(X - Sing_X)$. However, calculation of this group is non-trivial, but it can be simplified if a certain invariant of the branch curve of X - called the braid monodromy factorization - is known. This paper shows, taking the Cayley cubic as an example, how this fundamental group can be computed by using braid monodromy techniques and their liftings. This is one of the first examples that uses these techniques to calculate this sort of fundamental group.

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BibTeX RIS

M. Amram, M. Dettweiler, M. Friedman, M. Teicher. 2008-12-22. Fundamental group for the complement of the Cayley's singularities. https://arxiv.org/abs/0803.3005

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