A. Mark and J. Paupert [Presentations for cusped arithmetic hyperbolic lattices, 2018, arXiv:1709.06691.] presented a method to compute a presentation for any cusped complex hyperbolic lattice. In this note, we will use their method to give a presentation for the Eisenstein-Picard modular group in three complex dimensions.

Three gravity cores (LZK1, ZKA4, and CSJA6) from the incised Yangtze paleo-valley comprise a thick sequence of the post-glacial deposit. Nineteen genera (26 species) of the benthic foraminifers are described from these cores, with detailed down-core foraminiferal variations to investigate their paleoenvironmental implications. Three foraminiferal assemblages are recognized for the lower, middle, and upper parts of the cores respectively. The lower part is dominated by Ammonia beccarii var. and Florilus decorus with lower abundance and diversity. In the middle part, the foraminifers are abundant and diverse, dominated by both Ammonia beccarii var. and Elphidium advenum. Cavarotalia annectens, Pararotalia nipponica, and porcellaneous benthic foraminiferal forms are always present, sometimes abundant. The upper part is characterized by the Ammonia beccarii-Elphidium magellanicum assemblage, except for the Core ZKA4, which is barren of foraminifers in this interval. AMS 14C dates and foraminiferal assemblages both confirm that the transgression-regression sequence in these cores belongs to the “Ammonia transgression” during the Holocene. In addition to documenting the post-glacial sea-level fluctuations, the benthic foraminifers also reflect a warmer climate during the early–middle Holocene. The foraminiferal differences among the three cores can be used to interpret the influence of seawater during the post-glacial sea-level fluctuations. The area in the vicinity of Core ZKA4 was affected by marine water only during the middle Holocene, which was much shorter than the areas of the other cores.

In this paper, we will discuss the groups generated by two Heisenberg translations of $\text{PU}\left( 2,1 \right)$ and determine when they are free.

Little is known about the generators system of the higher dimensional Picard modular groups. In this paper, we prove that the higher dimensional Eisenstein–Picard modular group PU(3, 1;ℤ[ω3]) in three complex dimensions can be generated by four given transformations.

We prove that the Eisenstein–Picard modular group SU(2,1;ℤ[ω3]) can be generated by four given transformations.

In this note, we prove that the Gauss–Picard modular group PU(2,1;Θ1) has Property (FA). Our result gives a positive answer to a question by Stover [‘Property (FA) and lattices in SU(2,1)’, Internat. J. Algebra Comput.17 (2007), 1335–1347] for the group PU(2,1;Θ1).

J. W. Anderson (1996) asked whether two finitely generated Kleinian groups with the same set of axes are commensurable. We give some partial solutions.