A deformation theorem for Poincaré duality pairs in dimension 3
We prove the analogue of Johannson's Deformation Theorem for PD3 pairs.
math.GR↗
arXiv subjects
Gadde A. Swarup
Publications and source records attributed to Gadde A. Swarup.
Canonical decompositions for Poincaré duality pairs
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.
math.GR↗
Minimal cubings
We combine ideas of Scott and Swarup on good position for almost invariant subsets of a group with ideas of Sageev on constructing cubings from such sets. We construct cubings which are more canonical than in Sageev's original construction. We also show that almost invariant sets can be chosen to be in very good position.
math.GR↗
Delzant's variation on Scott complexity
We give an exposition of Delzant's ideas extending the notion of Scott complexity of finitely generated groups to surjective homomorphisms of finitely presented groups to finitely generated groups.
math.GR↗
A proof of a homeomorphism theorem of Waldhausen
We give a short proof of Waldhausen's homeomorphism theorem for orientable Haken 3-manifolds.
math.GT↗
Splittings of groups and intersection numbers
We prove algebraic analogues of the facts that a curve on a surface with self-intersection number zero is homotopic to a cover of a simple curve, and that two simple curves on a surface with intersection number zero can be isotoped to be disjoint.
math.GT↗
Canonical decompositions of 3-manifolds
We describe a new approach to the canonical decompositions of 3-manifolds along tori and annuli due to Jaco-Shalen and Johannson (with ideas from Waldhausen) - the so-called JSJ-decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus-torus theorems, and the theory of Seifert fibrations does not need to be developed in advance.
math.GT↗
An Algebraic Annulus Theorem
We present an extension of Dunwoody's theory of tracks and use it to prove an analogue of the annulus theorem for hyperbolic groups.
math.GR↗