Non-microstates free entropy dimension for groups

Geometric and Functional Analysis

Volumn 15, Issue 2, 2005, Pages 476-490

  Mineyev, Igor ^a   Shlyakhtenko, Dimitri ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23744503731     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-005-0513-z     Document Type: Article

References (18)

1. [A] L. AAGAARD, The non-microstates free entropy dimension of DT-operators, preprint available on-line at math.OA/0305397 (2003).
2. [At] M.F. ATIYAH, Elliptic operators, discrete groups and von Neumann algebras, Colloque "Analyse et Topologie" en l'Honneur de Henri Cartan (Orsay, 1974), Soc. Math. France, Paris, Astérisque 32/33 (1976), 43-72.
3. 2-Betti number, Potential Anal. 6:4 (1997), 313-326.
4. [BiCG] P. BIANE, M. CAPITAINE, A. GUIONNET, Large deviation bounds for matrix Brownian motion, Invent. Math. 152:2 (2003), 433-459.
5. 2-cohomology and group cohomology, Topology 25:2 (1986), 189-215.
6. 2-homology for von Neumann algebras, Preprint available on-line at math.OA/0309343 (2003).
7. [G1] D. GABORIAU, Coût des relations d'équivalence et des groupes, Invent. Math. 139 (2000), 41-98.
8. 2 de relations d'équivalence et de groupes, Publ. Math. Inst. Hautes Études Sci. 95 (2002), 93-150.
9. [GoHJ] F. GOODMAN, R. DE LA HARPE, V.F.R. JONES, Coxeter Graphs and Towers of Algebras, Springer-Verlag, 1989.
10. [J] K. JUNG, A free entropy dimension lemma, preprint math.OA/0207149 (2002).
11. 2-Betti numbers I: foundations, J. reine angew. Math 495 (1998), 135-162.
12. 2-Invariants: Theory and Applications to Geometry and K-Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], Springer-Verlag, Berlin, 44 (2002).
13. [MN] F.J. MURRAY, J. VON NEUMANN, On rings of operators, Ann. of Math. 37 (1936), 116-224.
14. [S] D. SHLYAKHTENKO, Some estimates for non-microstates free entropy dimension, with applications to q-semicircular families, Int. Math. Res. Notices 51 (2004), 2757-2772.
15. [V1] D.-V. VOICULESCU, The analogues of entropy and of Fisher's information measure in free probability theory II, Invent. Math. 118 (1994), 411-440.
16. [V2] D.-V. VOICULESCU, The analogues of entropy and of Fisher's information measure in free probability theory, III, GAFA, Geom. funct. anal. 6 (1996), 172-199.
17. [V3] D.-V. VOICULESCU, The analogues of entropy and of Fisher's information measure in free probability, V, Invent. Math. 132 (1998), 189-227.
18. [V4] D.-V. VOICULESCU, Free entropy, Bull. London Math. Soc. 34:3 (2002), 257-278.