Maps of degree 1 and Lusternik–Schnirelmann category

Rudyak, Yuli B.

doi:10.1016/j.topol.2017.02.061

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Cited by 7 publications

(2 citation statements)

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“…One of the classical applications of simplicial volume is an a priori estimate on mapping degrees [Gro82,Thu79,FM21]. In contrast, the exact relation between mapping degrees and monotonicity of (generalised) LS-category invariants is still wide open [Rud17,CLM20].…”

Section: 2mentioning

confidence: 99%

Bounded acyclicity and relative simplicial volume

Li¹,

Loeh²,

Moraschini³

2022

Preprint

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We provide new vanishing and glueing results for relative simplicial volume, following up on two current themes in bounded cohomology: The passage from amenable groups to boundedly acyclic groups and the use of equivariant topology.More precisely, we consider equivariant nerve pairs and relative classifying spaces for families of subgroups. Typically, we apply this to uniformly boundedly acyclic families of subgroups. Our methods also lead to vanishing results for ℓ 2 -Betti numbers of aspherical CW-pairs with small relative amenable category and to a relative version of a result by Dranishnikov and Rudyak concerning mapping degrees and the inheritance of freeness of fundamental groups.

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Section: 2mentioning

confidence: 99%

Bounded acyclicity and relative simplicial volume

Li¹,

Loeh²,

Moraschini³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…It's currently unknown whether this conjecture is true in general, but various special cases have been proven (e.g., see results in [10,12]), the most recent of which is the following theorem:…”

Section: Introductionmentioning

confidence: 99%