A note on graphs and rational balls

Lecuona, Ana G.

doi:10.1007/s13398-017-0464-x

RACSAM

2017

DOI: 10.1007/s13398-017-0464-x

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A note on graphs and rational balls

Ana G. Lecuona

Abstract: In this short note we study some particular graphs associated to small Seifert spaces and Montesinos links. The study of these graphs leads to new examples of Seifert manifolds bounding rational homology balls and Montesinos links bounding smoothly and properly embedded surfaces (possibly not orientable) in the 4 ball with Euler characteristic equal to 1.

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2023

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A survey of the homology cobordism group

Şavk

2023

Bull. Amer. Math. Soc.

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In this survey, we present the most recent highlights from the study of the homology cobordism group, with particular emphasis on its long-standing and rich history in the context of smooth manifolds. Further, we list various results on its algebraic structure and discuss its crucial role in the development of low-dimensional topology. Also, we share a series of open problems about the behavior of homology 3 3 -spheres and the structure of Θ Z 3 \Theta _{\mathbb {Z}}^3 . Finally, we briefly discuss the knot concordance group C \mathcal {C} and the rational homology cobordism group Θ Q 3 \Theta _{\mathbb {Q}}^3 , focusing on their algebraic structures, relating them to Θ Z 3 \Theta _{\mathbb {Z}}^3 , and highlighting several open problems. The appendix is a compilation of several constructions and presentations of homology 3 3 -spheres introduced by Brieskorn, Dehn, Gordon, Seifert, Siebenmann, and Waldhausen.

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A survey of the homology cobordism group

Şavk

2023

Bull. Amer. Math. Soc.

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show abstract

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A note on graphs and rational balls

Cited by 1 publication

References 9 publications

A survey of the homology cobordism group

A survey of the homology cobordism group

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