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Cubiquitous Lattices and Branched Covers bounding rational balls [PDF]

open access: yesarXiv
Greene and Owens explore cubiquitous lattices as an obstruction to rational homology 3-spheres bounding rational homology 4-balls. The purpose of this article is to better understand which sublattices of $\mathbb{Z}^n$ are cubiquitous with the aim of effectively using their cubiquity obstruction.
arxiv  

A Local-Global Study of Obstructed Deformation Problems -- I [PDF]

open access: yesarXiv
In this paper, we study possible obstructed deformations of 2-dimensional Galois Representations attached to newforms of weight 2 and level $N > 1$. We provide conditions on the existence of local and global obstructions, and explicit description of the Universal Deformation Ring in several cases.
arxiv  

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