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Preprints and Publications

 1. Dual homotopy invariants of G-foliations Thesis, University of Illinois at Urbana-Champaign, May 1980.

 2. Dual homotopy invariants of G-foliations Topology, 20(4):365--387, 1981.

 3. Homotopy invariants of foliations (with Franz W. Kamber) In Topology Symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979). Lecture Notes in Math. Vol. 788, pages 49--61. Springer, Berlin, 1980.

 4. On the homotopy and cohomology of the classifying space of Riemannian foliations Proc. Amer. Math. Soc. 81 (1981), no. 3, 485--489.

 5. On the secondary classes of foliations with trivial normal bundles Comment. Math. Helv. 56 (1981), no. 2, 307--326.

 6. Growth of leaves and secondary invariants of foliations preprint, Princeton University, 1982

 7. Independent rigid secondary classes for holomorphic foliations Invent. Math. 66 (1982), no. 2, 313--323.

 8. Exotic classes for measured foliations Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 2, 389--391.

 9. The Godbillon-Vey class for analytic foliations of codimension one preprint, Princeton University, 1983

 10. Vanishing of secondary classes for compact foliations J. London Math. Soc. (2) 28 (1983), no. 1, 175--183.

 11. Global invariants for measured foliations Trans. Amer. Math. Soc. 280 (1983), no. 1, 367--391.

 12. The Weil measures of foliations - a survey and some applications preprint, Princeton University, 1983

 13. Secondary classes, Weil measures and the geometry of foliations. (with James L. Heitsch) J. Differential Geom. 20 (1984), no. 2, 291--309.

 14. Secondary classes and transverse measure theory of a foliation (with Anatole Katok) Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 2, 347--350.

 15. The classifying space of smooth foliations Illinois J. Math. 29 (1985), no. 1, 108--133.

 16. Foliation dynamics and leaf invariants Comment. Math. Helv. 60 (1985), no. 2, 319--335.

 17. Problems on rigidity of group actions and cocycles Ergodic Theory Dynam. Systems 5 (1985), no. 3, 473--484.

 18. The Jacobian cocycle of a distal group action. preprint, Math. Sci. Res. Inst., 1985.

 19. The Godbillon measure of amenable foliations J. Differential Geom. 23 (1986), no. 3, 347--365.

 20. The Connes spectrum for actions of abelian groups on continuous-trace algebras (with Dorte Olesen, Iain Raeburn, and Jonathan Rosenberg) Ergodic Theory Dynam. Systems 6 (1986), no. 4, 541--560.

 21. Ergodic theory and Weil measures for foliations (with Anatole Katok) Ann. of Math. (2) 126 (1987), no. 2, 221--275.

 22. The ∂-operator Appendix A in Global analysis on foliated spaces by C. C. Moore and C. Schochet, Springer, New York, 1988.

 23. Toeplitz operators and the eta invariant: the case of $S^1$ (with Ronald G. Douglas and Jerome Kaminker) in Index theory of elliptic operators, foliations, and operator algebras (New Orleans, LA/Indianapolis, IN, 1986), 11--41, Contemp. Math., 70, Amer. Math. Soc., Providence, RI, 1988.

 24. Ergodic theory of foliations and a theorem of Sacksteder in Dynamical systems (College Park, MD, 1986--87), 291--328, Lecture Notes in Math., 1342, Springer, Berlin, 1988.

 25. Spectral theory of foliation geometric operators preprint, U.I.C., 1989

 26. Eta invariants and von Neumann algebras (with Ronald G. Douglas and Jerome Kaminker) Bull. Amer. Math. Soc. (N.S.) 21 (1989), no. 1, 83--87.

 27. Eta invariants and the odd index theorem for coverings in Geometric and topological invariants of elliptic operators (Brunswick, ME, 1988), 47--82, Contemp. Math., 105, Amer. Math. Soc., Providence, RI, 1990.

 28. Homotopy characteristic classes of foliations (with Daniel Lehmann) Illinois J. Math. 34 (1990), no. 3, 628--655.

 29. Differentiability, rigidity and Godbillon-Vey classes for Anosov flows (with Anatole Katok) Inst. Hautes Études Sci. Publ. Math. No. 72 (1990), 5--61 (1991).

 30. Deformation rigidity for subgroups of SL(n, Z) acting on the n-torus Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 1, 107--113.

 31. Cyclic cocycles, renormalization and eta-invariants. (with Ronald G. Douglas and Jerome Kaminker) Invent. Math. 103 (1991), no. 1, 101--179.

 32. The longitudinal cocycle and the index of Toeplitz operators (with Ronald G. Douglas and Jerome Kaminker) J. Funct. Anal. 101 (1991), no. 1, 120--144.

 33. Exceptional minimal sets of $C^{1+a}$-group actions on the circle Ergodic Theory Dynam. Systems 11 (1991), no. 3, 455--467.

 34. The intersection product of transverse invariant measures (with Yoshihiko Mitsumatsu) Indiana Univ. Math. J. 40 (1991), no. 4, 1169--1183.

 35. Almost Compact Foliations. preprint, U.I.C., 1991

 36. Rigidity for Anosov actions of higher rank lattices Ann. of Math. (2) 135 (1992), no.2, 361--410.

 37. Rigidity for Cartan actions of higher rank lattices (with Anatole Katok, Jim Lewis, and Robert J. Zimmer) preprint, U.I.C., 1991

 38. Affine Anosov actions Michigan Math. J. 40 (1993), no. 3, 561--575.

 39. A product theorem for $\Omega B\Gamma_G$ Topology and Its Applications, 50 (1993), no. 1, 81--86.

 40. Topology of covers and the spectral theory of geometric operators in Index theory and operator algebras (Boulder, CO, 1991), 87--119, Contemp. Math., 148, Amer. Math. Soc., Providence, RI, 1993.

 41. The transverse Euler class for amenable foliations (with Yoshihiko Mitsumatsu) preprint, U.I.C., 1993

 42. Exotic theory for foliated spaces preprint, U.I.C., 1993

 43. Topological rigidity of strong stable foliations for Cartan actions Ergodic Theory Dynam. Systems {\bf 14} (1994), no.~1, 151--167.

 44. Pure-point spectrum for foliation geometric operators (with Jésus Alvarez Lopez) preprint, U.I.C., 1994

 45. Differential topology, foliations, and group actions (with Paul A. Schweitzer, Nathan Moreira dos Santos, and José Luis Arraut, editors) Contemp. Math., 161, Amer. Math. Soc., Providence, RI, 1994.

 46. Transverse Euler classes of foliations on nonatomic foliation cycles (with Yoshihiko Mitsumatsu) in Differential topology, foliations, and group actions (Rio de Janeiro, 1992), 29--39, Contemp. Math., 161, Amer. Math. Soc., Providence, RI, 1994.

 47. A survey of rigidity theory for Anosov actions in Differential topology, foliations, and group actions (Rio de Janeiro, 1992), 143--173, Contemp. Math., 161, Amer. Math. Soc., Providence, RI, 1994.

 48. Coarse geometry of foliations in Geometric study of foliations (Tokyo, 1993), 35--96, World Sci. Publishing, River Edge, NJ, 1994.

 49. Infinitesimal rigidity for hyperbolic actions J. Differential Geom. 41 (1995), no. 3, 515--527.

 50. Exotic index theory and the Novikov conjecture in Novikov conjectures, index theorems and rigidity, Vol. 2 (Oberwolfach, 1993), 255--276, Cambridge Univ. Press, Cambridge, 1995.

 51. Manifolds which cannot be leaves of foliations (with Oliver Attie) Topology 35 (1996), no. 2, 335--353.

 52. Coarse cohomology for families (with James L. Heitsch) Illinois Jour. Math. 45 (2001), no. 2, 323--360.

 53. Expansive maps of the circle (with Chris Connell and Alex Furman) UIC preprint 2000

 54. Dynamics and the Godbillon-Vey class: a history and survey. in Foliations: geometry and dynamics (Warsaw, 2000), 29--60, World Sci. Publishing, River Edge, NJ, 2002.

 55. Tangential LS category and cohomology for foliations (with Hellen Colman) in Foliations: geometry and dynamics (Warsaw, 2000), 29--60, World Sci. Publishing, River Edge, NJ, 2002.

 56. LS-category of compact Hausdorff foliations (with Hellen Colman) Trans. Amer. Math. Soc. 356 (2004), no.~1, 1463--1487.

 57. Category and compact leaves Topology and Its Applications 153 (2006), 2135--2154.

 58. Foliation Geometry/Topology Problem Set preprint, U.I.C., 2003

 59. Dynamics and the Godbillon-Vey Class of C^1 Foliations (with Remi Langevin) Journal Math. Society Japan, Vol. 70:423 - 462, 2018. revision of 2004 preprint

 60. Compact foliations with finite transverse LS category (with Pawel Walczak) Journal Math. Society Japan, Vol. 70:1015-1046, 2018; revision of 2005 preprint

 63. Hirsch foliations in codimension greater than one (with Andrzej Bís and Joseph Shive) In FOLIATIONS 2005, pages 71--108, World Scientific, 2006.

 64. Foliations Lodz 2005 Problem Set In FOLIATIONS 2005, pages 441--475, World Scientific, 2006.

 65. FOLIATIONS 2005 Proceedings Conference held June 14-23, Lodz, Poland Editors: Steven Hurder, Remi Langevin , Takashi Tsuboi , Pawel Walczak World Scientific, 2006.

 66. Transverse LS-category for Riemannian foliations (with Dirk Toben) Transactions AMS 361 (2009), 5647-5680.

 67. The equivariant LS-category of polar actions (with Dirk Toben) Topology and Its Applications 156 (2009), 500-514.

 68. Classifying foliations In Foliations, Geometry, and Topology, Contemp. Math., Vol. 498, pages 1-65, Amer. Math. Soc., Providence, RI, 2009.

 69. Characteristic classes for Riemannian foliations In Differential Geometry, pages 11-35, World Sci. Publ., Hackensack, NJ, 2009.

 70. Lectures on Foliation Dynamics: Barcelona 2010 In Foliations: Dynamics, Geometry and Topology, Advanced Courses in Mathematics CRM Barcelona, 2014.

 71. Embedding solenoids in foliations (with Alex Clark) Topology and Its Applications, Vol. 158 (2011), 1249-1270.

 72. Homogeneous matchbox manifolds (with Alex Clark) Transactions A.M.S., Vol. 365 (2013), 3151-3191.

 73. Voronoi tessellations for matchbox manifolds (with Alex Clark and Olga Lukina) Topology Proceedings, Vol. 41 (2013), 167-259.

 74. The dynamics of generic Kuperberg flows (with Ana Rechtman) Astérisque, Vol. 377, 2016.

 75. Shape of matchbox manifolds (with Alex Clark and Olga Lukina) Indagationes Mathematicae, Vol. 25:669-712, 2014

 76. Classifying matchbox manifolds (with Alex Clark and Olga Lukina) Geometry and Topology, to appear {arXiv:1311.0226}

 77. Lipshitz matchbox manifolds Geometry, Dynamics, and Foliations 2013, Advanced Studies in Pure Math. Vol. 72, 2017, pages 71-115.

 78. Problem Session - FOLIATIONS 2012 In FOLIATIONS 2012, pages 235-255, World Scientific, 2013.

 79. The discriminant invariant of Cantor group actions (with Jessica Dyer and Olga Lukina) Topology and Its Applications, Vol. 208 (2016), 64-92.

 80. Growth and homogeneity of matchbox manifolds (with Jessica Dyer and Olga Lukina) Indagationes Mathematicae, Vol. 28 (2017), 145-169.

 81. Aperiodicity at the boundary of chaos (with Ana Rechtman) Ergodic Theory Dynamical Systems, Vol. 38:2683-2728, 2018.

 82. Perspectives on Kuperberg flows (with Ana Rechtman) Topology Proceedings, Vol. 51:197-244, 2017.

 83. Molino theory for matchbox manifolds (with Jessica Dyer and Olga Lukina) Pacific Journal Math., Vol. 289:91-151, 2017.

 84. Wild solenoids (with Olga Lukina) Transactions A.M.S., Vol. 371:4493-4533, 2019 {arXiv:1702.03032}

 85. Manifold-like matchbox manifolds (with Alex Clark and Olga Lukina) Proceedings A.M.S., Vol. 147:3579-3594, 2019, {arXiv:1704.04402}

 86. Orbit equivalence and classification of weak solenoids (with Olga Lukina) Indiana Univ. Math. J., Vol. 69:2339-2363, 2020; {arXiv:1803.02098}.

 87. Pro-groups and a generalization of a theorem of Bing (with Alex Clark and Olga Lukina) Topology and Its Applications, Vol. 270, ; {arXiv:1811.00288}.

 88. Limit group invariants for non-free Cantor actions (with Olga Lukina) Ergodic Theory Dynamical Systems, vol. 41, 1751-1794; {arXiv:1904.11072}.

 89. Nilpotent Cantor actions (with Olga Lukina) Proceedings A.M.S., to appear; {arXiv:1905.07740}.

 90. Cantor dynamics of renormalizable groups (with Olga Lukina and Wouter van Limbeek) Groups, Geometry, and Dynamics, to appear; {arXiv:2002.01565}.

 91. The prime spectra of solenoidal manifolds (with Olga Lukina) submitted, {arXiv:2103.06825}.

 **. Entropy and Dynamics of C^1 Foliations preprint, U.I.C., August 2000

updated July 5, 2021