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Cluster Algebras - Lauren K. Williams, Sergey Fomin, Andrei Zelevinsky
Cluster Algebras - Lauren K. Williams, Sergey Fomin, Andrei Zelevinsky
Involve, a Journal of Mathematics Vol. 16, No. 3, 2023
Involve, a Journal of Mathematics Vol. 16, No. 3, 2023
Hyperbolic Handlebody Complements in 3-Manifolds
Hyperbolic Handlebody Complements in 3-Manifolds
Let $M_0$ be a compact and orientable 3-manifold. After capping off spherical boundaries with balls and removing any torus boundaries, we prove that the resulting manifold $M$ contains handlebodies of arbitrary genus such that the closure of their complement is hyperbolic. We then extend the octahedral decomposition to obtain bounds on volume for some of these handlebody complements.
Intrinsically Knotted Graphs and Connected Domination
Intrinsically Knotted Graphs and Connected Domination
We classify all the maximal linklessly embeddable graphs of order 12 and show that their complements are all intrinsically knotted. We derive results about the connected domination numbers of a graph and its complement. We provide an answer to an open question about the minimal order of a 3-non-compliant graph. We prove that the complements of knotlessly embeddable graphs of order at least 15 are all intrinsically knotted. We provide results on general $k$-non-compliant graphs and leave a set of open questions for further exploration of the subject.
Hyperbolicity and Volume of Hyperbolic Bongles
Hyperbolicity and Volume of Hyperbolic Bongles
We consider a simple but infinite class of staked links known as bongles. We provide necessary and sufficient conditions for these bongles to be hyperbolic. Then, we prove that all balanced hyperbolic $n$-bongles have the same volume and the corresponding volume is an upper bound on the volume of any hyperbolic $n$-bongle for $n$ even. Moreover, all hyperbolic $n$-bongles have volume strictly less than $5n(1.01494\dots)$. We also include explicit volume calculations for all hyperbolic 3-bongles through 6-bongles.
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CityWalk
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Disney Springs
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Top BearBops 2022
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Top BearBops 2022
Playlist ¡ BinaryBunny ¡ 101 items
Essential Instrumental
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Essential Instrumental
Playlist ¡ BinaryBunny ¡ 334 items ¡ 2 saves
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