Bounded cohomology of transformation groups

Brandenbursky, Michael; Marcinkowski, Michał

doi:10.48550/arxiv.1902.11067

Cited by 3 publications

(15 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2) is, essentially, the same formula that appears in [2], as well as in [10] and other places. Minor differences in appearance are the result of different conventions in the definition of (bounded) cohomology.…”

Section: The Transfer Induced By a Left-cofinite Couplingmentioning

confidence: 55%

“…In all cases the proof strategy is to meet the requirements of the following lemma. While its part i is directly taken from [2], our new results in degree > 3 rely on part ii. The trick of applying the Kronecker pairing to compensate for the lack of a Künneth formula in bounded cohomology was previously used in [7].…”

Section: Proof Of the Main Resultsmentioning

confidence: 99%

“…To obtain the coupling and the sequences of group homomorphisms required by the previous lemma, we follow the constructions of Brandenbursky-Marcinkowski [2], respectively Kimura [6], with only some slight modifications. For the convenience of the reader we present the full argument, adapted to the setting of couplings between groups.…”

Section: It Remains To Show That Dim Trmentioning

confidence: 99%

“…All these groups are given the discrete topology. Building upon a construction of Gambaudo and Ghys [4], Brandenbursky and Marcinkowski [2] on the level of ordinary and bounded cohomology. With the help of these maps they showed that for certain fundamental groups π 1 (M ) the exact reduced bounded cohomology EH * b (Homeo vol,0 (M )) contains EH * b (F 2 ) as a subspace and, in particular, is infinitedimensional in degree 3.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Higher-degree bounded cohomology of transformation groups

Nitsche

2021

Preprint

View full text Add to dashboard Cite

For M a compact Riemannian manifold Brandenbursky and Marcinkowski constructed a transfer map H * b (π1(M )) → H * b (Homeo vol,0 (M )) and used it to show that for certain M the space EH 3b (Homeo vol,0 (M )) is infinite-dimensional. Kimura adapted the argument to Diff vol (D 2 , ∂D 2 ). We extend both results to the higher degrees EH 2n b , n ≥ 1. We also show that for certain M the ordinary cohomology H * (Homeo vol,0 (M )) is non-trivial in all degrees. In our computations we view the transfer map as being induced by a coupling of groups.

show abstract

Section: The Transfer Induced By a Left-cofinite Couplingmentioning

confidence: 55%

Section: Proof Of the Main Resultsmentioning

confidence: 99%

Section: It Remains To Show That Dim Trmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Higher-degree bounded cohomology of transformation groups

Nitsche

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…There is few results on the third bounded cohomology [5,13]. Recently, Brandenbursky and Marcinkowski [3] proved that EH 3 b (Diff Ω (M )) is uncountably infinitedimensional for a complete Riemannian manifold M with a volume form Ω with a certain condition on π 1 (M ). Corollary 1.2 does not covered by their result since π 1 (D 2 ) is trivial.…”

Section: Introductionmentioning

confidence: 99%