%0 Journal Article %1 koberdasuciu2020residually %A Koberda, Thomas %A Suciu, Alexander I. %D 2020 %J Communications in Contemporary Mathematics %K %N 3 %P 1950016 (44 pages). %R 10.1142/S0219199719500160 %T Residually finite rationally p groups %U http://arxiv.org/abs/1604.02010 %V 22 %X In this article we develop the theory of residually finite rationally $p$ (RFR$p$) groups, where $p$ is a prime. We first prove a series of results about the structure of finitely generated RFR$p$ groups (either for a single prime $p$, or for infinitely many primes), including torsion-freeness, a Tits alternative, and a restriction on the BNS invariant. Furthermore, we show that many groups which occur naturally in group theory, algebraic geometry, and in $3$-manifold topology enjoy this residual property. We then prove a combination theorem for RFR$p$ groups, which we use to study the boundary manifolds of algebraic curves $CP^2$ and in $C^2$. We show that boundary manifolds of a large class of curves in $C^2$ (which includes all line arrangements) have RFR$p$ fundamental groups, whereas boundary manifolds of curves in $CP^2$ may fail to do so.

@article{koberdasuciu2020residually, abstract = {In this article we develop the theory of residually finite rationally $p$ (RFR$p$) groups, where $p$ is a prime. We first prove a series of results about the structure of finitely generated RFR$p$ groups (either for a single prime $p$, or for infinitely many primes), including torsion-freeness, a Tits alternative, and a restriction on the BNS invariant. Furthermore, we show that many groups which occur naturally in group theory, algebraic geometry, and in $3$-manifold topology enjoy this residual property. We then prove a combination theorem for RFR$p$ groups, which we use to study the boundary manifolds of algebraic curves $\mathbb{CP}^2$ and in $\mathbb{C}^2$. We show that boundary manifolds of a large class of curves in $\mathbb{C}^2$ (which includes all line arrangements) have RFR$p$ fundamental groups, whereas boundary manifolds of curves in $\mathbb{CP}^2$ may fail to do so.}, added-at = {2023-12-13T10:49:36.000+0100}, author = {Koberda, Thomas and Suciu, Alexander I.}, biburl = {https://www.bibsonomy.org/bibtex/274b43b5c65845ec3c314788bfdadcf16/admin}, doi = {10.1142/S0219199719500160}, interhash = {db4a1c34d01a575104ae81b7309a2724}, intrahash = {74b43b5c65845ec3c314788bfdadcf16}, journal = {Communications in Contemporary Mathematics}, keywords = {}, month = apr, number = 3, pages = {1950016 (44 pages).}, timestamp = {2023-12-13T10:49:36.000+0100}, title = {Residually finite rationally p groups}, url = {http://arxiv.org/abs/1604.02010}, volume = 22, year = 2020 }