Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0703890

Canonical decompositions for Poincaré duality pairs

Peter Scott·Gadde A. Swarup
View original source ↗Read source document ↗Export metadata ↓

Abstract

The authors previously described an algebraic analogue of the JSJ-decomposition of a 3-manifold. This analogue is defined for any finitely presented, one-ended group. We study this analogue in the special case of Poincaré duality pairs.

Explore related subjects

math.GRmath.GT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Peter Scott, Gadde A. Swarup. 2020-04-11. Canonical decompositions for Poincaré duality pairs. https://arxiv.org/abs/math/0703890

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Strongly Regular Graphs of Rank Four

Strongly regular graphs are regular graphs with a constant number of common neighbours between adjacent vertices, and a constant number of common neighbours between non-adjacent vertices. These graphs have been of great interest over the last few decades and often give rise to interesting groups of automorphisms. In this paper we take a reverse approach, and leverage strong classification results on rank four permutation groups to classify the strongly regular graphs which yield such groups as a group of automorphisms.

math.GR↗
arXiv2026

Every finite group admits a just finite presentation

A finite presentation < X | R > of a finite group is called `just finite' if removing any relation from R results in a presentation for an infinite group. It has been an open question (Kourovka Notebook, Problem 21.10) whether every finite group admits such a presentation. We resolve this conjecture in the affirmative.

math.GR↗
arXiv2026

Assouad--Nagata dimension of systolic complexes with almost flat intervals

We introduce the notion of systolic complexes with almost flat intervals. They constitute a subclass of fit systolic complexes and arise naturally in the study of graphical C(3)--T(6) small cancellation complexes. We prove that their Assouad--Nagata dimension is bounded above by a universal constant. As consequences, we obtain universal bounds on the Assouad--Nagata dimension of tame simply connected graphical C(3)--T(6) small cancellation complexes and of finitely generated groups defined by graphical C(3)--T(6) small cancellation presentations. In the appendix, we observe that the proof of finiteness of asymptotic dimension for buildings due to Dymara and Schick also yields finiteness of their asymptotic Assouad--Nagata dimension.

math.GR↗