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Krishna Siddhi - One of the best experts on this subject based on the ideXlab platform.
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Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
'Wiley', 2020Co-Authors: Krishna SiddhiAbstract:We construct taut foliations in every closed 3-manifold obtained by $r$-framed Dehn surgery along a Positive 3-braid knot $K$ in $S^3$, where $r < 2g(K)-1$ and $g(K)$ denotes the Seifert genus of $K$. This confirms a prediction of the L-space Conjecture. For instance, we produce taut foliations in every non-L-space obtained by surgery along the pretzel knot $P(-2,3,7)$, and indeed along every pretzel knot $P(-2,3,q)$, for $q$ a Positive Odd Integer. This is the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hyperbolic L-space knots. Additionally, we construct taut foliations in every closed 3-manifold obtained by $r$-framed Dehn surgery along a Positive 1-bridge braid in $S^3$, where $r
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Taut foliations, Positive braids, and the L-space conjecture:
'Boston College University Libraries', 2020Co-Authors: Krishna SiddhiAbstract:Thesis advisor: Joshua E. GreeneWe construct taut foliations in every closed 3-manifold obtained by r-framed Dehn surgery along a Positive 3-braid knot K in S^3, where r < 2g(K)-1 and g(K) denotes the Seifert genus of K. This confirms a prediction of the L--space conjecture. For instance, we produce taut foliations in every non-L-space obtained by surgery along the pretzel knot P(-2,3,7), and indeed along every pretzel knot P(-2,3,q), for q a Positive Odd Integer. This is the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hyperbolic L-space knots. We adapt our techniques to construct taut foliations in every closed 3-manifold obtained along r-framed Dehn surgery along a Positive 1-bridge braid, and indeed, along any Positive braid knot, in S^3, where r < g(K)-1. These are the only examples of theorems producing taut foliations in surgeries along hyperbolic knots where the interval of surgery slopes is in terms of g(K).Thesis (PhD) — Boston College, 2020.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Mathematics
Frédéric Rochon - One of the best experts on this subject based on the ideXlab platform.
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Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds
Mathematische Zeitschrift, 2020Co-Authors: Werner Müller, Frédéric RochonAbstract:For $$d=2n+1$$ d = 2 n + 1 a Positive Odd Integer, we consider sequences of arithmetic subgroups of $${\text {SO}}_0(d,1)$$ SO 0 ( d , 1 ) and yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.
Rochon Frédéric - One of the best experts on this subject based on the ideXlab platform.
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Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds
2019Co-Authors: Mueller Werner, Rochon FrédéricAbstract:For d=2n+1 a Positive Odd Integer, we consider sequences of arithmetic subgroups of SO_0(d,1) and Spin(d,1) yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.Comment: 27 pages, added an upper bound for sequences of representation
Werner Müller - One of the best experts on this subject based on the ideXlab platform.
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Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds
Mathematische Zeitschrift, 2020Co-Authors: Werner Müller, Frédéric RochonAbstract:For $$d=2n+1$$ d = 2 n + 1 a Positive Odd Integer, we consider sequences of arithmetic subgroups of $${\text {SO}}_0(d,1)$$ SO 0 ( d , 1 ) and yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.
Mueller Werner - One of the best experts on this subject based on the ideXlab platform.
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Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds
2019Co-Authors: Mueller Werner, Rochon FrédéricAbstract:For d=2n+1 a Positive Odd Integer, we consider sequences of arithmetic subgroups of SO_0(d,1) and Spin(d,1) yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.Comment: 27 pages, added an upper bound for sequences of representation