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math.GT2010★ 4 cited
Algebraic characterization of simple closed curves via Turaev's cobracket
Moira Chas, Fabiana Krongold
The vector space $\V$ generated by the conjugacy classes in the fundamental group of an orientable surface has a natural Lie cobracket $\mapδ{\V}{\V\times \V}$. For negatively curv…
math.GT2008
An algebraic characterization of simple closed curves on surfaces with boundary
Moira Chas, Fabiana Krongold
We characterize in terms of the Goldman Lie algebra which conjugacy classes in the fundamental group of a surface with non empty boundary are represented by simple closed curves. W…