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Thickstun, Thomas

 thickstun
Contact Information
Thomas L. Thickstun, Ph.D.
Professor


Office: MCS 551
Email: tt04@txstate.edu
Phone: 512.245.3428
 
Research Interest
Low Dimensional Topology

Professor Thickstun received his Ph.D. from University of California in 1974. He has worked primarily on non-compact 3-manifolds and on the resolution of topological singularities in dimension three. A recent partial result on the Resolution Conjecture (obtained in collaboration with R. J. Daverman) has yielded the first characterization (modulo the Poincare Conjecture) of 3-manifolds among arbitrary topological spaces.


Selected Publications:

  • Thickstun, T. L.; A further extension of the loop theorem and resolutions of generalized 3-manifolds whose singular sets have general position dimension one, (to appear in Topology and Its Applications).
  • Daverman, R.J.; Thickstun, T. L.; The 3-manifold recognition problem. Trans. Amer. Math. Soc. 358 (2006), no. 12, 5257--5270.
  • Kavichcholi, A.; Repovsh, D.; Tikstun, T.; Geometric topology of generalized 3-manifolds. (Russian) Fundam. Prikl. Mat. 11 (2005), no. 4, 71--84.
  • Thickstun, T. L.; Resolutions of generalized 3-manifolds whose singular sets have general position dimension one. Topology Appl. 138 (2004), no. 1-3, 61--95.
  • Funar, L.; Thickstun, T. L. On open 3-manifolds proper homotopy equivalent to geometrically simply-connected polyhedra. Topology Appl. 109 (2001), no. 2, 191--200.
  • Brin, Matthew G.; Thickstun, T. L.; 3-manifolds which are end 1-movable. Mem. Amer. Math. Soc. 81 (1989), no. 411, 73 pp.
  • Thickstun, T. L.; Strongly acyclic maps and homology 3-manifolds with 0-dimensional singular set. Proc. London Math. Soc. (3) 55 (1987), no. 2, 378--432.
  • Brin, Matthew G.; Thickstun, T. L.; Open, irreducible 3-manifolds which are end 1-movable. Topology 26 (1987), no. 2, 211--233.
  • Brin, Matthew G.; Thickstun, T. L.; On properly embedding noncompact surfaces in arbitrary 3-manifolds. Proc. London Math. Soc. (3) 54 (1987), no. 2, 350--366.
  • Thickstun, T. L.; Special volume in honor of R. H. Bing (1914--1986). Edited by S. Singh and T. L. Thickstun. Topology Appl. 24 (1986), no. 1-3. Elsevier Science B.V., Amsterdam, 1986. pp. i--iv and 1--271. 54-06.
  • Brin, Matthew G.; Thickstun, T. L.; On the proper Steenrod homotopy groups, and proper embeddings of planes into 3-manifolds. Trans. Amer. Math. Soc. 289 (1985), no. 2, 737--755.
  • Thickstun, T. L.; An extension of the loop theorem and resolutions of generalized 3-manifolds with 0-dimensional singular set. Invent. Math. 78 (1984), no. 2, 161--222.
  • Thickstun, T. L.; Low-dimensional topology. Proceedings of the Conference on Topology in Low Dimension held at the University College of North Wales, Bangor, July 2--5, 1979. Edited by R. Brown [Ronald Brown] and T. L. Thickstun. London Mathematical Society Lecture Note Series, 48. Cambridge University Press, Cambridge-New York, 1982. iii+246 pp. ISBN: 0-521-28146-6 57-06.
  • Thickstun, T. L.; Open acyclic 3-manifolds, a loop theorem and the Poincaré conjecture. Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 2, 192--194.
  • McMillan, D. R., Jr.; Thickstun, T. L. Open three-manifolds and the Poincare conjecture. Topology 19 (1980), no. 3, 313--320.
  • Thickstun, T. L.; Taming and the Poincaré conjecture. Trans. Amer. Math. Soc. 238 (1978), 385--396.
  • Hilden, Hugh M.; Montesinos, Jose M.; Thickstun, Thomas; Closed oriented 3-manifolds as 3-fold branched coverings of $S^3$ of special type. Pacific J. Math. 65 (1976), no. 1, 65--76.