PreprintCC0arXiv
The integral homology of SL2(ℤ[1/n])
Abstract
Let ℤ[1/n] := {a/nr: a ∈ ℤ,r ∈ ℤ ≥ 0} be the euclidean domain obtained from the ring of integers ℤ by localizing at n. Moreover, let SL2(ℤ[1/n]) be the group of all invertible 2-by-2 matrices of determinant one with entries in ℤ[1/n]. The homology groups Hk(SL2(ℤ[1/n]),ℤ) are of interest in Geometric Group Theory, Algebraic Number Theory and Algebraic K-theory. In this dissertation, we study these groups via a spectral sequence derived by the action of SL2(ℤ[1/n]) on the product of the trees Bp associated with the p-adic valuation on ℚ where p is a prime factor of n.
Related
BibTeX
@misc{picinini2026integral,
title = {{The integral homology of $\textSL_2(\mathbbZ[1/n])$}},
author = {Isadora Vanzella Picinini},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.25633},
eprint = {2608.25633},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.25633},
note = {CC0},
}
RIS
TY - UNPB
TI - The integral homology of SL_2(ℤ[1/n])
AU - Isadora Vanzella Picinini
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.25633
UR - https://arxiv.org/abs/2608.25633
AB - Let ℤ[1/n] := {a/n^r: a ∈ ℤ,r ∈ ℤ ≥ 0} be the euclidean domain obtained from the ring of integers ℤ by localizing at n. Moreover, let SL_2(ℤ[1/n]) be the group of all invertible 2-by-2 matrices of determinant one with entries in ℤ[1/n]. The homology groups H_k(SL_2(ℤ[1/n]),ℤ) are of interest in Geometric Group Theory, Algebraic Number Theory and Algebraic K-theory. In this dissertation, we study these groups via a spectral sequence derived by the action of SL_2(ℤ[1/n]) on the product of the trees B_p associated with the p-adic valuation on ℚ where p is a prime factor of n.
ER -