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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. |
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. |
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. |
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. |
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, Vol. 23:1-27, 2019; {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., vol. 150, 289-304, 2022; {arXiv:1905.07740}. |
90. | Cantor dynamics of renormalizable groups | |
(with Olga Lukina and Wouter van Limbeek) | ||
Groups, Geometry, and Dynamics, vol. 15, 1449-1487, 2021; {arXiv:2002.01565}. |
91. | The prime spectra of solenoidal manifolds | |
(with Olga Lukina) | ||
submitted, {arXiv:2103.06825}. |
92. | Kuperberg dreams | |
(with Ana Rechtman) | ||
celebratio.org/Kuperberg_KM; {arXiv:2103.06825}. |
93. | Essential holonomy of Cantor actions | |
(with Olga Lukina) | ||
Journal Math. Society Japan, to appear; {arxiv:2205.06285} |
94. | Type invariants for solenoidal manifolds | |
(with Olga Lukina) | ||
submitted, May 1, 2023; {arXiv:2305.00863} |
95. | Prime spectrum and dynamics for nilpotent Cantor actions | |
(with Olga Lukina) | ||
Pacific Journal Mathematics, to appear; {arXiv:2305.00896} |
96. | Characteristic classes of flat Diff(M) foliations | |
preprint, November 2023; {arXiv:2311.09160} |
**. | Entropy and Dynamics of C^1 Foliations | |
preprint, U.I.C., August 2000 |
updated December 7, 2023