Annales Mathématiques
Blaise Pascal
no. 1
Integral foliated simplicial volume and ergodic decomposition
[Volume simplicial feuilleté intégral et décomposition ergodique]
Clara Löh1 ; Giovanni Sartori2
1 Fakultät für Mathematik Universität Regensburg 93040 Regensburg
2 Maxwell Institute and Department of Mathematics Heriot-Watt University Edinburgh EH14 4AS
Annales mathématiques Blaise Pascal, Tome 31 (2024) no. 1, pp. 47-64.

Nous établissons une formule d’intégration pour le volume simplicial feuilleté intégral sur des décompositions ergodiques. Celle-ci est analogue à la formule de décomposition ergodique pour le coût des groupes.

We establish an integration formula for integral foliated simplicial volume along ergodic decompositions. This is analogous to the ergodic decomposition formula for the cost of groups.

Publié le :
DOI : 10.5802/ambp.425
Classification : 55N10, 55N35, 28D15
Keywords: Integral foliated simplicial volume, ergodic decomposition
Mot clés : Volume simplicial feuilleté intégral, décomposiiton ergodique

Clara Löh 1 ; Giovanni Sartori 2

1 Fakultät für Mathematik Universität Regensburg 93040 Regensburg
2 Maxwell Institute and Department of Mathematics Heriot-Watt University Edinburgh EH14 4AS
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Clara Löh; Giovanni Sartori. Integral foliated simplicial volume and ergodic decomposition. Annales mathématiques Blaise Pascal, Tome 31 (2024) no. 1, pp. 47-64. doi : 10.5802/ambp.425. https://ambp.centre-mersenne.org/articles/10.5802/ambp.425/

[1] Miklós Abért; Nikolay Nikolov Rank gradient, cost of groups and the rank versus Heegaard genus problem, J. Eur. Math. Soc., Volume 14 (2012) no. 5, pp. 1657-1677 | DOI | Zbl

[2] Caterina Campagnolo; Diego Corro Integral foliated simplicial volume and circle foliations, J. Topol. Anal., Volume 15 (2023) no. 1, pp. 155-184 | DOI | MR | Zbl

[3] Daniel Fauser Integral foliated simplicial volume and S 1 -actions, Forum Math., Volume 33 (2021) no. 3, pp. 773-788 | DOI | Zbl

[4] Daniel Fauser; Clara Löh; Marco Moraschini; José P. Quintanilha Stable integral simplicial volume of 3-manifolds, J. Topol., Volume 14 (2021) no. 2, pp. 608-640 | DOI | Zbl

[5] Roberto Frigerio; Clara Löh; Cristina Pagliantini; Roman Sauer Integral foliated simplicial volume of aspherical manifolds, Isr. J. Math., Volume 216 (2016), pp. 707-751 | DOI | Zbl

[6] Damien Gaboriau Coût des relations d’équivalence et des groupes, Invent. Math., Volume 139 (2000) no. 1, pp. 41-98 | DOI | Zbl

[7] Misha Gromov Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, 152, Birkhäuser, 1999, xx+585 pages (Based on the 1981 French original, with appendices by M. Katz, P. Pansu and S. Semmes, translated from the French by Sean Michael Bates) | Zbl

[8] Alexander S. Kechris Global Aspects of Ergodic Group Actions, Mathematical Surveys and Monographs, 160, American Mathematical Society, 2010, xii+237 pages | DOI

[9] Alexander S. Kechris Classical Descriptive Set Theory, Graduate Studies in Mathematics, 156, Springer, 2012

[10] Alexander S. Kechris; Benjamin D. Miller Topics in Orbit Equivalence, Lecture Notes in Mathematics, 1852, Springer, 2004, x+134 pages | DOI

[11] Robion C. Kirby; Larry C. Siebenmann On the triangulation of manifolds and the Hauptvermutung, Bull. Am. Math. Soc., Volume 75 (1969), pp. 742-749 | DOI | Zbl

[12] John M. Lee Introduction to smooth manifolds, Graduate Texts in Mathematics, 218, Springer, 2013, xvi+708 pages

[13] Clara Löh Cost vs. integral foliated simplicial volume, Groups Geom. Dyn., Volume 14 (2020) no. 3, pp. 899-916 | DOI | Zbl

[14] Clara Löh; Marco Moraschini; Roman Sauer Amenable covers and integral foliated simplicial volume, New York J. Math., Volume 28 (2022), pp. 1112-1136 | Zbl

[15] Clara Löh; Cristina Pagliantini Integral foliated simplicial volume of hyperbolic 3-manifolds, Groups Geom. Dyn., Volume 10 (2016), pp. 825-865 | Zbl

[16] John Milnor On spaces having the homotopy type of a CW -complex, Trans. Am. Math. Soc., Volume 90 (1959), pp. 272-280 | DOI | Zbl

[17] Marco Schmidt L 2 -Betti Numbers of ℛ-Spaces and the Integral Foliated Simplicial Volume, Ph. D. Thesis, Westfälische Wilhelms-Universität Münster (2005) (http://nbn-resolving.de/urn:nbn:de:hbz:6-05699458563)

[18] Larry C. Siebenmann On the homotopy type of compact topological manifolds, Bull. Am. Math. Soc., Volume 74 (1968), pp. 738-742 | DOI | Zbl

[19] Veeravalli S. Varadarajan Groups of automorphisms of Borel spaces, Trans. Am. Math. Soc., Volume 109 (1963), pp. 191-220 | DOI | Zbl

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