E-prints

  1. (with Hayden, Huang, Ruberman and Sunukjian) Exotic aspherical 4-manifolds, pdf, arXiv:2411.19400v2
  2. (with J. Huang) Bordifications of hyperplane arrangements and their curve complexes, J. of Topology 14 (2) (2021), 419--451. pdf,   arXiv:2003.13553
  3. (with G. Le, K. Schreve) Action dimensions of some simple complexes of groups, J. of Topology 12 (2019), 1266-1314.  pdf, arXiv:1803.04095v1, published
  4. (with J. Huang) Determining the action dimension of an Artin group by using its complex of abelian subgroup, Bull. London. Math. Soc. (2017) pdf  arXiv:1608.03572 , published.
  5. (with P. Kropholler) Criteria for asphericity of polyhedral products: corrigenda to ``Right-angularity, flag complexes, asphericity'', Geom. Dedicata 179 (2015) 39--44. pdf,  arXiv:1102.4670, published.
  6. (with G. Avramidi, B. Okun, K. Schreve) The action dimension of right-angled Artin groups, Bull. London Math. Soc. 48 (1) (2016), 115--126.  pdf, arXiv: 1409.6325, published
  7. (with A. Edmonds) Euler characteristics of generalized Haken manifolds, Alg. & Geom. Topology 14 (2014),  3701--3716. pdf, arXiv: 1402.7096, published
  8. When are two Coxeter orbifolds diffeomorphic? Mich. Math. J. 63 (2014), 401--421.   pdf, arXiv:1306.6046, published
  9. The geometry and topology of Coxeter groups, in Introduction to Modern Mathematics, ALM 33, Higher Education Press, Beijing--Boston, 2015, pp. 145--158  pdf
  10. (with J. Fowler and J. Lafont) Aspherical manifolds that cannot be triangulated, Alg. & Geom. Topology 14 (2014), 795--803.  pdf,  arXiv:13043730, published
  11. (with M. Kahle) Random graph products of finite groups are rational duality groups, J. of Topology 7 (2014), 589--606. pdf, arXiv, published
  12. (with S. Settepanella) Vanishing results for the cohomology of complex toric hyperplane complements, Pub. Mat. 57 (2013), 379--392. pdf,  arXiv:1111.2866, published
  13. Right angularity, flag complexes, asphericity, Geom. Dedicata 159 (2012), 239--262.  pdf, arXiv, published
  14. The Euler characteristic of a polyhedral product, Geom. Dedicata 159 (2012), 263--266.  pdf,  arXiv, published
  15. (with T. Januszkiewicz and J. Lafont) 4-dimensional locally CAT(0)-manifolds with no Riemannian smoothings, Duke Math. J., 161 (2012), 1--28.  pdf,  arXiv, published
  16. (with B. Okun) Cohomology computations for Artin groups, Bestvina-Brady groups and graph products, Groups Geom. Dyn. 6 (2012) 485--531.  pdf,  arXiv, final version
  17. (with T. Januszkiewicz, I.J. Leary and B. Okun) Cohomology of hyperplane complements with group ring coefficients, IMRN (2011), 2110--2116.  pdf, arXiv
  18. Examples of buildings constructed via covering spaces, Groups, Geom. Dyn. 3 (2009), 279-298.  pdf 
  19. Lectures on orbifolds and reflection groups, Transformation Groups and Moduli Spaces of Curves (eds, L. Ji, S-T Yau) International Press, 2010, pp. 63--93.  pdf
  20. (with J. Dymara, T. Januszkiewicz, J. Meier and B. Okun) Compactly supported cohomology of buildings, Comment. Math. Helv. 85 (2010), 551--582.  pdf, arXiv
  21. The Hopf Conjecture and the Singer Conjecture, Guido's Book of Conjectures (ed. I. Chatterji) Monographie de L'Enseignement Math. 40 (2008), pp. 80-82.  pdf
  22. (with T. Januszkiewicz and I. Leary) The L2-cohomology of hyperlane complements, Groups Geom. Dyn. 1 (2007) 301--309. pdf,  arXiv
  23. (with J. Dymara, T. Januszkiewicz and B. Okun) Cohomology of Coxeter groups with group ring coefficients: II, Algebraic & Geometric Topology 6 (2006), 1289-1318. pdf,  arXiv
  24. (with J. Dymara, T. Januszkiewicz and B. Okun)   Weighted L2-cohomology of Coxeter groups, Geometry & Topology 11 (2007), 47-138. pdf,  arXiv
  25. (with J. Meier)  Reflection groups and CAT(0) complexes with exotic local structures, High-dimensional Manifold Topology (eds. F.T. Farrell and W. Luck),World Scientific, New Jersey, 2003, 151-158. pdf  ps
  26. (with B. Okun)   L2 -homology of right-angled Coxeter groups associated  to barycentric subdivisions, Topology and Its Applications 140 (2004), 197-202. pdf    ps
  27. (with I. Leary)   Some examples of discrete group actions on aspherical manifolds, High-dimensional Manifold Topology (eds. F.T. Farrell and W. Luck),World Scientific, New Jersey, 2003, 139-150. pdf
  28. (with I. Leary)   L2-cohomology of Artin groups, J.  London Math. Soc. 68 (2003), 493--510. pdf,   published
  29. (with T. Januszkiewicz and R. Scott)  Fundamental groups of blow-ups, Advances in Math. 177 (2003), 115-179. pdf  ps arXiv
  30. (with J. Meier)  The topology at infinity of Coxeter groups and buildings, Comment. Math. Helv. 77 (2002), 746-766.   pdf, Correction.  pdf
  31. Exotic aspherical manifolds,  School on High-dimensional Manifold Topology, ICTP, Trieste 2002. pdf
  32. Nonpositive curvature and reflection groups, in The Handbook  of Geometric Topology, eds. R. Daverman and R. Sher), Elsevier, Amsterdam, 2002, 373-422.  pdf  ps
  33. (with T. Januszkiewicz and S. Weinberger)  Relative hyperbolization and aspherical bordisms, an addendum to “Hyperbolization of Polyhedra,” J. of Differential Geometry 58 (2001),  535-541. pdf
  34. (with B. Okun)  Vanishing theorems and conjectures for the L2-homology of the right-angled Coxeter groups, Geometry & Topology 5 (2001), 7-74. pdf ps arXiv
  35. (with R. Charney) When is a Coxeter system determined by its Coxeter group? J. London Math. Soc. 61 (2000), 441--461. pdf
  36. (with T. Januszkiewicz)  Right-angled Artin groups are commensurable with right-angled Coxeter groups, J. of Pure and Applied Algebra 153 (2000), 229-235.  pdf  
  37. Poincaré duality groups, in Surveys in Surgery Theory, Volume 1 (eds. S. Cappell, A. Ranicki, J. Rosenberg) Annals of Math. Studies, 145, Princeton University Press, Princeton, 2000, 167-193.  pdf
  38.  (with B. Okun and F. Zheng) Piecewise Euclidean structures and Eberlein’s Rigidity Theorem in the singular case, Geometry and Topology  3 (1999), 303-330.  pdf arXiv
  39. (with G. Moussong)  Notes on nonpositively curved polyhedra, in Low Dimensional Topology (eds. K. Boroczky, W. Neumann, A. Stipicz), Bolyai
    Society Math. Studies 8, Janos Bolyai Math. Soc., Budapest, 1999, 11-94.  pdf  ps
  40. Buildings are CAT(0), Geometry and Cohomology in Group Theory (eds P. Kropholler and R. Stohr) London Math. Soc. Lecture Notes 252, Cambridge Univ. Press (1998), 108-123.  pdf
  41. The cohomology of a Coxeter group with group ring coefficients, Duke Math. J. 91 (1998), 297-313. pdf  95 (1998), 635. correction
  42. (with T. Januszkiewicz and R. Scott) Nonpositive curvature of blow-ups, Selecta Math. New series 4 (1998), 491--547. pdf  ps  selecta.pdf
  43. (with F.D. Ancel and C.R. Guilbault) CAT(0) reflection manifolds, AMS/IP Studies in Advanced Math. 2 (1997), 441--445.  pdf
  44. (with R. Charney and G. Moussong)  Nonpositively curved piecewise Euclidean structures on hyperbolic manifolds, Michigan Math. J. 44 (1997), 201-208.    dvi    ps    pdf
  45. (with R. Charney)   Finite K(\pi,1)'s for Artin groups, in Prospects in Topology, ed. by F. Quinn, Annals of Math Studies 138, Princeton Univ. Press (1995), 110-124.    dvi    ps    pdf   
  46. (with R. Charney)  The polar dual of a convex polyhedral set in hyperbolic space, Michigan Math. J. 42 (1995), 479-509.    dvi    ps    pdf   published Correction, 43 (1996), 619.   pdf
  47. (with R. Charney)  The K(\pi,1)-problem for hyperplane complements associated to infinite reflection groups, J. of AMS 8 (1995), 597-627.    dvi    ps    pdf   pdf from JSTOR
  48. (with R. Charney)  On the Euler characteristic of a nonpositively curved piecewise Euclidean manifold, Pacific J. of Math. 171 (1995), 117-137.    dvi    ps    pdf
  49. (with R. Charney) Strict hyperbolization, Topology 34 (1995), 329--350.  pdf
  50. (with R. Charney) Singular metrics of nonpositive curvature on branched covers of Riemannian manifolds, Amer. J. Math. 115 (1993), 929-1009. pdf (from JSTOR)
  51. (with R. Charney) Reciprocity of growth functions of Coxeter groups, Geom. Dedicata 39 (1991), 373-378.  pdf
  52. (with M. Shapiro) Coxeter groups are almost convex, Geom. Dedicata 39 (1991), 55-57.  pdf
  53. (with T. Januszkiewicz) Hyperbolization of polyhedra, J. Diff. Geom. 34 (1991), 347--388.  pdf
  54. (with T. Januszkiewicz) Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. Journal, 62, (1991), 417--451.  pdf  (3.8 MB)
  55. (with J-C. Hausmann) Aspherical manifolds without smooth or PL structure, Springer Lecture Notes in Math. 1370, (1989), 135--142.  pdf
  56. Regular convex cell complexes, in Geometry and Topology, Marcel Dekker (1987), 53-88.  pdf  (2.6 MB)
  57. The homology of a space on which a reflection group acts, Duke Math. Journal 55, (1987), 97--104.  pdf  Erratum 56 (1988), 221. pdf
  58. Some aspherical manifolds, Duke Math. Journal 55, (1987), 105--139.  pdf  (3.1 MB)
  59. A hyperbolic 4-manifold, Proc. of AMS 93 (1985), 325-328. pdf (from JSTOR), pdf (what should have been published)
  60. Coxeter groups and aspherical manifolds, Springer Lecture Notes in Math. 1051 (1984) 197--221.  pdf
  61. (with J. Morgan) Finite group actions on homotopy 3-spheres, in The Smith Conjecture, Academic Press (1984), 181--225.  pdf  (5.2 MB)
  62. A survey of results in higher dimensions, ibid, 227--240.  pdf (1.7 MB)
  63. Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983), 293-324. pdf (from JSTOR)
  64. Some group actions on homotopy spheres of dimension seven and fifteen, Amer. J. Math. 104 (1982), 59-90. pdf (from JSTOR)
  65. Universal G-manifolds, Amer. J. Math. 103 (1981), 103-141. pdf (from JSTOR)
  66. (with W.C. Hsiang and J. Morgan) Concordance classes of regular O(n) actions on homotopy spheres, Acta Math. 144 (1980), 153--221.  pdf  (6.3 MB)
  67. (with W.C. Hsiang and W.Y. Hsiang) Differentiable actions of compact simple groups on homotopy spheres and Euclidean spaces, in Symposia in Pure Math. 32, AMS (1978) 313--323.  pdf  (1.1 MB)
  68. Smooth G-manifolds as collections of fiber bundles, Pac. Jour. of Math. 77, No. 2, (1978), 315-363. pdf
  69. (with W.C. Hsiang) Concordance classes of regular U(n) and Sp(n) actions on homotopy spheres, Ann. of Math. 105 (1977), 325-341. pdf (from JSTOR)
  70. Smooth actions of the classical groups, Princeton University PhD thesis, 1974.   pdf (16.4 MB)
  71. Examples of actions on manifolds almost diffeomorphic to Vn+1,2 , Springer Lecture Notes in Math. 298 (1972), 301--317. pdf
  72. Group actions on exotic Stiefel manifolds, Princeton University senior thesis, 1971.  pdf (5.6 MB)
Books: Infinite group actions on polyhedra, Ergebnisse der mathematik und Grenzgebiete 3 Folge 77, Springer 2024. pdf
            The Geometry and Topology of Coxeter Groups, London Math. Soc. Monograph Series 32, Princeton University Press, Princeton, 2007.  pdf
            Multiaxial Actions on Manifolds, Springer Lecture Notes in Math.  643, Springer, 1978.  pdf

Abstracts (Oberwolfach Reports):  a) Weighted L2-cohomology of Coxeter groups, Oberwolfach Reports, vol. 3 (2), 1169-1219, 19/2006. pdf   b) Cohomology of Coxeter groups with group ring coefficients, Oberwolfach  Reports, vol. 3 (4) 2579-2630, 43/2006. pdf  c) Compactly supported cohomology of buildings, Oberwolfach Reports, vol. 5 (1) 119-172  3/2008. pdf  d) Cohomology computations for relatives of Coxeter groups, vol. 7 1165-1224, 20/2010.  pdf   Action dimension of some simple complexes of groups pdf

Book Review: Combinatorics of Coxeter Groups (by Bjorner and Brenti) Bulletin of the AMS, 45 (2008), 445-449. pdf

Gabor Moussong's thesis:  Hyperbolic Coxeter Groups, OSU, 1988. better.pdf   pdf
Igor Iskhakov's thesis:  On hyperbolic surface tessellations and equivariant spacelike polyhedral surfaces in Minkowski space, OSU, 2000.  pdf
Dan Boros' thesis: L2-homology of low-dimensional buildings, OSU, 2003. pdf   or Ohio Link
Dongwen Qi's thesis: On irreducible, infinite, non-affine Coxeter groups, OSU, 2007. pdf  or Ohio Link
Aliska Gibbins' thesis: Automorphisms of buildings constructed via covering spaces, 2013.  pdf
Ryan Greene's thesis: The deformation theory of discrete reflection groups and projective structures, 2013. pdf
Giang Le's thesis: The action dimension of Artin groups, 2016. pdf
Two unpublished papers by Glen Bredon from 1973 on biaxial actions:  Regular O(n)-actions and the twist suspension of knots. pdf
    Classification of regular actions of the classical groups with three orbit types. pdf


(with M. Shapiro) Coxeter groups are automatic (1991 preprint with gap in proof of "Parallel Wall Theorem"). pdf