Generalizations of Agol’s inequality and nonexistence of tight laminations

Kuessner, Thilo

doi:10.2140/pjm.2011.251.109

Cited by 2 publications

(2 citation statements)

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“…We assert that τ ∩ r k ij : r k ij ∈ P (i, j) is the full 1-skeleton of a subsimplex of τ . This means, we have to check the following claim: 9 ) belong to τ1 ∪ ij P (i, j). We will prove this assertion for [x, z], assuming x = z.…”

Section: Proofmentioning

confidence: 99%

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Multicomplexes, Bounded Cohomology and Additivity of Simplicial Volume

Kuessner¹

2015

Bulletin of the Korean Mathematical Society

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Abstract. We discuss some additivity properties of the simplicial volume for manifolds with boundary: we give proofs of additivity for glueing amenable boundary components and of superadditivity for glueing amenable submanifolds of the boundary, and we discuss doubling of 3-manifolds.This paper is devoted to the behaviour of simplicial volume under cutting and pasting along amenable submanifolds. Such results have been proved by Gromov in [3], for closed manifolds ([3], Section 3) by fairly elementary arguments, and for open manifolds ([3], Section 4) by much more advanced arguments. The aim of this article is to write complete proofs for the case of compact manifolds with boundary, using elementary arguments which are closer to the arguments that were needed for the closed case.The simplicial volume is a homotopy invariant of compact manifolds. It was defined in [3], using the l 1 -norm on singular chains, as follows.

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Section: Proofmentioning

confidence: 99%

“…The generalization of Lemma 5 resp. Lemma 6 to locally finite chains (and disconnected intersections) will be needed in [9] and can be used to generalize Theorem 1 for the simplicial volume of noncompact manifolds for cut and paste along compact submanifolds.…”

Section: Locally Finite Chainsmentioning

confidence: 99%