Mixed t\^ete-\`a-t\^ete twists as monodromies associated with holomorphic function germs
Abstract
T\^ete-\`a-t\^ete graphs were introduced by N. A'Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed t\^ete-\`a-t\^ete graphs provide a generalization which define mixed t\^ete-\`a-t\^ete twists, which are pseudo-periodic automorphisms on surfaces. We characterize the mixed t\^ete-\`a-t\^ete twists as those pseudo-periodic automorphisms that have a power which is a product of right-handed Dehn twists around disjoint simple closed curves, including all boundary components. It follows that the class of t\^ete-\`a-t\^ete twists coincides with that of monodromies associated with reduced function germs on isolated complex surface singularities.
Keywords
Cite
@article{arxiv.1712.05988,
title = {Mixed t\^ete-\`a-t\^ete twists as monodromies associated with holomorphic function germs},
author = {Pablo Portilla Cuadrado and Baldur Sigurðsson},
journal= {arXiv preprint arXiv:1712.05988},
year = {2020}
}
Comments
21 pages, 14 figures. Minor corrections. Version as accepted in journal. arXiv admin note: text overlap with arXiv:1706.05580