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Given a digraph, an ordering of its vertices defines a backedge graph, namely the undirected graph whose edges correspond to the arcs pointing backwards with respect to the order. The degreewidth of a digraph is the minimum over all ordering of the m
Externí odkaz:
http://arxiv.org/abs/2407.19270
Autor:
Simon, Christopher-Lloyd, Stucky, Ben
We introduce a $1$-player game called \emph{pin the loop} and analyse its complexity. A loop is a generic immersion of the circle in a surface, considered up to isotopy. A loop is taut when it is minimally intersecting in its homotopy class. A pinnin
Externí odkaz:
http://arxiv.org/abs/2405.16216
The modular group $\operatorname{PSL}_2(\mathbb{Z})$ acts on the upper-half plane $\mathbb{HP}$ with quotient the modular orbifold, uniformized by the function $\mathfrak{j} \colon \mathbb{HP}\to \mathbb{C}$. We first show that second derived subgrou
Externí odkaz:
http://arxiv.org/abs/2402.17628
Autor:
Simon, Christopher-Lloyd
A filoop is a generic immersion of a circle in a closed oriented surface, whose complement is a disjoint union of discs, considered up to orientation preserving diffeomorphisms. It gives rise to a chord diagram C which has an interlace graph G, calle
Externí odkaz:
http://arxiv.org/abs/2310.08806
Autor:
Simon, Christopher-Lloyd
The modular group PSL(2;Z) acts on the hyperbolic plane HP with quotient the modular surface M, whose unit tangent bundle U is a 3-manifold homeomorphic to the complement of the trefoil knot in the 3-sphere. The hyperbolic conjugacy classes of PSL(2;
Externí odkaz:
http://arxiv.org/abs/2211.05957
Autor:
Simon, Christopher-Lloyd
We first describe, over a field K of characteristic different from 2, the orbits for the adjoint actions of the Lie groups PGL(2, K) and PSL(2, K) on their Lie algebra sl(2, K). While the former are well known, the latter lead to the resolution of ge
Externí odkaz:
http://arxiv.org/abs/2210.02481
Autor:
Simon, Christopher-Lloyd
We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.
Comment: 32 pages, in French
Comment: 32 pages, in French
Externí odkaz:
http://arxiv.org/abs/2106.15450
Publikováno v:
Geom. Topol. 28 (2024) 593-625
We study the space of measured laminations ML on a closed surface from the valuative point of view. We introduce and study a notion of Newton polytope for an algebraic function on the character variety. We prove for instance that trace functions have
Externí odkaz:
http://arxiv.org/abs/2104.04340
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