Minimally intersecting filling pairs on the punctured surface of genus two

Jeffreys, Luke

doi:10.1016/j.topol.2018.12.011

Cited by 2 publications

(3 citation statements)

References 5 publications

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“…The effect of the vertex transposition on the boundary components of the ribbon graph associated to the filling pair diagram is shown in Figure 4. 15. We see that we have one boundary component with 8(j + k) + 8 sides corresponding to a zero of order 2(j + k) + 1, and a second boundary component with 8(j + k) sides corresponding to a zero of order 2(j + k) − 1, if x = 8j − 6, or 8(j + k) + 8 sides corresponding to a zero of order 2(j + k) + 1, if x = 8j + 2.…”

Section: Strata Of the Form H(2k)mentioning

confidence: 99%

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Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs

Jeffreys

2021

Trans. Amer. Math. Soc.

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In every connected component of every stratum of Abelian differentials, we construct square-tiled surfaces with one vertical and one horizontal cylinder. We show that for all but the hyperelliptic components this can be achieved in the minimum number of squares necessary for a square-tiled surface in that stratum. For the hyperelliptic components, we show that the number of squares required is strictly greater and construct surfaces realising these bounds. Using these surfaces, we demonstrate that pseudo-Anosov homeomorphisms optimising the ratio of Teichmüller to curve graph translation length are, in a reasonable sense, ubiquitous in the connected components of strata of Abelian differentials. Finally, we present a further application to filling pairs on punctured surfaces by constructing filling pairs whose algebraic and geometric intersection numbers are equal.

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Section: Strata Of the Form H(2k)mentioning

confidence: 99%

“…We define i g,p to be the minimal geometric intersection number for a filling pair on S g,p . The values of i g,p were determined in the works of Aougab-Huang [1], Aougab-Taylor [3], and the author [15], and can be summarised as follows.…”

Section: Filling Pairs On Punctured Surfacesmentioning

confidence: 99%

Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs

Jeffreys

2021

Trans. Amer. Math. Soc.

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Section: Filling Pairs On Punctured Surfacesmentioning

confidence: 99%

Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs

Jeffreys¹

2019

Preprint

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In every connected component of every stratum of Abelian differentials, we construct square-tiled surfaces with one vertical and one horizontal cylinder. We show that for all but the hyperelliptic components this can be achieved in the minimum number of squares necessary for a square-tiled surface in that stratum. For the hyperelliptic components, we show that the number of squares required is strictly greater and construct surfaces realising these bounds.Using these surfaces, we demonstrate that pseudo-Anosov homeomorphisms optimising the ratio of Teichm üller to curve graph translation length are, in a reasonable sense, ubiquitous in the connected components of strata of Abelian differentials. Finally, we present a further application to filling pairs on punctured surfaces by constructing filling pairs whose algebraic and geometric intersection numbers are equal.

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Minimally intersecting filling pairs on the punctured surface of genus two

Cited by 2 publications

References 5 publications

Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs

Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs

Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs

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