Show Summary Details
More options …

Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

Online
ISSN
1435-5337
See all formats and pricing
More options …

The cup product of Brooks quasimorphisms

Michelle Bucher
/ Nicolas Monod
Published Online: 2018-02-14 | DOI: https://doi.org/10.1515/forum-2017-0237

Abstract

We prove the vanishing of the cup product of the bounded cohomology classes associated to any two Brooks quasimorphisms on the free group. This is a consequence of the vanishing of the square of a universal class for tree automorphism groups.

MSC 2010: 20J06; 20E05; 20J05

References

• [1]

R. Brooks, Some remarks on bounded cohomology, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, Ann. of Math. Stud. 97, Princeton University Press, Princeton (1981), 53–63. Google Scholar

• [2]

M. Bucher and N. Monod, The bounded cohomology of $S{L}_{2}$ over local fields and S-integers, Int. Math. Res. Not. IMRN (2017), 10.1093/imrn/rnx096. Google Scholar

• [3]

B. Duchesne and N. Monod, Group actions on dendrites and curves, preprint (2016), https://arxiv.org/abs/1609.00303v2.

• [4]

R. I. Grigorchuk, Some results on bounded cohomology, Combinatorial and Geometric Group Theory (Edinburgh 1993), London Math. Soc. Lecture Note Ser. 204, Cambridge University Press, Cambridge (1995), 111–163. Google Scholar

• [5]

T. Hartnick and P. Schweitzer, On quasioutomorphism groups of free groups and their transitivity properties, J. Algebra 450 (2016), 242–281.

• [6]

N. Heuer, Cup product in bounded cohomology of the free group, preprint (2017), https://arxiv.org/abs/1710.03193.

• [7]

B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972), 1–96. Google Scholar

• [8]

Y. Mitsumatsu, Bounded cohomology and ${l}^{1}$-homology of surfaces, Topology 23 (1984), no. 4, 465–471. Google Scholar

• [9]

N. Monod, Continuous Bounded Cohomology of Locally Compact Groups, Lecture Notes in Math. 1758, Springer, Berlin, 2001. Google Scholar

• [10]

N. Monod and Y. Shalom, Negative curvature from a cohomological viewpoint and cocycle superrigidity, C. R. Math. Acad. Sci. Paris 337 (2003), no. 10, 635–638.

• [11]

N. Monod and Y. Shalom, Cocycle superrigidity and bounded cohomology for negatively curved spaces, J. Differential Geom. 67 (2004), no. 3, 395–455.

• [12]

A. H. Rhemtulla, A problem of bounded expressibility in free products, Proc. Camb. Philos. Soc. 64 (1968), 573–584.

• [13]

R. A. Ryan, Introduction to Tensor Products of Banach Spaces, Springer Monogr. Math., Springer, London, 2002. Google Scholar

Published Online: 2018-02-14

Published in Print: 2018-09-01

Citation Information: Forum Mathematicum, Volume 30, Issue 5, Pages 1157–1162, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

Export Citation

© 2018 Walter de Gruyter GmbH, Berlin/Boston.