Publications - Martin Scharlemann

Math Reviews of these papers (requires MathSciNet license)

A preprint accessible below may differ somewhat from its final published version.
  1. (With R. Kirby) A curious category which equals TOP. Manifolds- Tokyo-1973: Proceedings of the 1973 Tokyo conference on the topology of manifolds, University of Tokyo, 1975, 93-97.
  2. (With L. Siebenmann) The Hauptvermutung for smooth singular homeomorphisms. Manifolds-Tokyo-1973: Proceedings of the 1973 Tokyo conference on the topology of manifolds, University of Tokyo, 1975, 85-91.
  3. (With L. Siebenmann) The Hauptvermutung for smooth homeomorphisms II: A proof valid for open 4-manifolds. Compositio Math. 29 (1974) 253-263.
  4. Equivalence of 5-dimensional s-cobordisms. Proc. AMS 53 (1975) 508-510.
  5. Simplicial Triangulation of non-combinatorial manifolds of dimension less than nine. Trans. Am. Math. Soc. 219 1 (1976) 269-287.
  6. Constructing strange manifolds with the dodecahedral space. Duke Math. J. 43 (1976) 33-40.
  7. Transversality theories at dimension 4. Inventiones Math. 33 (1976) 1-14.
  8. (With R. C. Kirby) Eight faces of the Poincare homology 3-sphere in Geometric Topology ed. by James C. Cantrell, Academic Press, 1979, pp. 113-146.
  9. Thoroughly knotted homology spheres. Houston J. Math. 3 (1977) 271-283.
  10. The fundamental group of fibered knot cobordisms. Math. Ann. 225 (1977) 243-251.
  11. Isotopy and cobordism of homology spheres in spheres. J. London Math. Soc. 16 (1977) 559-567.
  12. Non-PL imbeddings of 3-manifolds. Amer. J. Math. 100 (1978) 539-546.
  13. Approximating CAT CE maps by CAT homeomorphisms. in Geometric Topology ed. by James C. Cantrell, Academic Press, 1979, pp. 475-501.
  14. Smooth CE maps and smooth homeomorphisms. in Algebraic and Geometric Topology, ed. by Kenneth Millett, Lecture notes in Mathematics #664, Springer, 1978, pp. 234-240.
  15. Transverse Whitehead triangulations. Pacific J. Math. 80 (1979) 245-251.
  16. Subgroups of SL(2,R) freely generated by three parabolic elements Linear and Multilinear Algebra 7 (1979) 177-191.
  17. Essential tori in 4-manifold boundaries. Pacific J. Math. 105 (1983) 439-447.
  18. The subgroup of Δ2 generated by torus automorphisms. Math. Ann. 251 (1980) 263-268.
  19. The complex of curves on non-orientable surfaces. J. London Math. Soc. 25 (1982) 171-184.
  20. (With Craig Squier) Automorphisms of the free group of rank two without finite orbits. AMS Contemporary Mathematics Series 20 (1983) 341-346.
  21. Tunnel number one knots satisfy the Poenaru conjecture. Topology and its Applications. 18 (1984) 235-258.
  22. The four-dimensional Schoenflies conjecture is true for genus two imbeddings. Topology 23 (1984) 211-217.
  23. Outermost forks and a theorem of Jaco. AMS Contemp. Math. 44 (1985) 189-193.
  24. 3-manifolds with H2(A, ∂A) = 0 and a conjecture of Stallings. in Knot theory and manifolds, Lecture notes in Math. #1144, Springer, 1985, pp. 138-145.
  25. Smooth Spheres in R4 with four critical points are standard. Inventiones Math. 79 (1985) 125-141.
  26. Unknotting number one knots are prime. Inventiones Math. 82 (1985) 37-55.
  27. (With S. Bleiler) Tangles, Property P and a problem of J. Martin Math. Ann. 273 14 (1986) 215-255.
  28. The Thurston norm and 2-handle addition. Proc. Am. Math. Soc. 100 (1987) 362-366.
  29. (With S. Bleiler) A projective plane in R4 with three critical points is standard. Topology 27 (1988) 519-540.
  30. A remark on companionship and property P. Proc. Am. Math. Soc. 98 (1986) 169-170.
  31. Sutured manifolds and generalized Thurston norms, Jour. Diff. Geometry, 29 (1989) 557-614.
  32. (With A. Thompson) Unknotting number, genus, and companion tori. Math. Ann. 280 (1988) 191-205.
  33. (With A. Thompson) Finding disjoint Seifert surfaces Bull. Lon. Math. Soc. 20 (1988) 61-64.
  34. (With A. Thompson) Link genus and the Conway moves. Commentarii Math. Helvetici 64 (1989) 527-535.
  35. Producing reducible 3-manifolds by surgery on a knot. Topology 29 (1990) 481-500.
  36. (With A. Thompson) Detecting unknotted graphs in 3-space . Jour. Diff. Geom. 34 (1991) 539-560.
  37. Planar graphs, family trees, and braids. in Progress in Knot Theory and related Topics, M. Boileau, M. Domergue, Y. Mathieu & K. Millett, eds., Hermann, 1997, 29-50.
  38. Some pictorial remarks on Suzuki's Brunnian graph. in Topology '90 - Proc. of Ohio State Topology Year, B. Apanasov, W. D. Neumann, A. W. Reid and L. Siebenmann, eds., Walter de Gruyter, 1992, 351-354.
  39. Handlebody complements in the 3-sphere: A remark on a theorem of Fox. Proc. Amer. Math. Soc. 115(1992) 1115-1117.
  40. Unknotting via simultaneous crossing changes. Trans. Amer. Math. Soc. 336 (1993) 855-868.
  41. Lectures on the theory of sutured manifolds. in Korea Advanced Inst. of Technology Workshop Proceedings, 1990, pp. 25-46.
  42. (With A. Thompson) Heegaard splittings of (surface) x I are standard. Math. Ann. 295 (1993) 549-564.
  43. Topology of knots. in Topological Aspects of the Dynamics of Fluids and Plasmas, H. K. Moffatt, G. M. Zaslavsky, P. Comte, M. Tabor, eds., Kluwer Academic Publishers, 1992, pp. 65-82.
  44. (With Y. Q. Wu) Hyperbolic manifolds and degenerating handle additions. J. Austral. Math. Soc. 55 (1993) 72-89.
  45. (With A. Thompson) Pushing arcs and graphs around in handlebodies in Proceedings of the Knoxville low-dimensional topology conference, International Press, 1994, 163-171.
  46. (With A. Thompson) Thin position and Heegaard splittings of the 3- sphere. Jour. Diff. Geom. 39 (1994) 343-357.
  47. (With A. Thompson) Thin position for 3-manifolds. AMS Contemporary Math. 164 (1994) 231-238.
  48. (With H. Rubinstein) Comparing Heegaard splittings of non-Haken 3- manifolds. Topology, 35 (1996) 1005-1026.
  49. (With Anneke Bart) Least weight injective surfaces are fundamental. Topology & its Applications 69 (1995) 251- 264.
  50. (With H. Rubinstein) Transverse Heegaard splittings. Mich. Math Jour. 44 (1997) 69-83.
  51. (With H. Rubinstein) Comparing Heegaard splittings - the bounded case . Trans. AMS, 350 (1998) 689-715.
  52. Local detection of strongly irreducible Heegaard splittings, Topology and its Applications. 90 (1998) 135-147.
  53. Heegaard splittings of compact 3-manifolds, Handbook of geometric topology, ed by R. Daverman and R. Sherr, 921--953, North-Holland, Amsterdam, 2002.
  54. Crossing Changes, Chaos, Solitons, and Fractals, 9 (1998) 693-704.
  55. (With H. Rubinstein) Genus two Heegaard splittings of orientable 3-manifolds Proceedings of the 1998 Kirbyfest, Geometry and Topology Monographs 2 (1999) 489-553.
  56. (With J. Schultens) The tunnel number of the connect sum of n knots is at least n, Topology 38 (1999) 265-270.
  57. (With J. Schultens) Comparing Heegaard and JSJ structures of orientable 3-manifolds, Trans. Amer. Math. Soc. 353 (2001) 557-584.
  58. (With D. Cooper) The structure of a solvmanifold's Heegaard splittings, Proceedings of the Gökova Geometry-Topology Conference 1998 (also in Turkish Journal of Mathematics 23 (1999)) 1-18.
  59. (With M. Jones) How a strongly irreducible Heegaard splitting intersects a handlebody, Topology and its Applications 110 (2001) 289-301
  60. (With J. Schultens) Annuli in generalized Heegaard splittings and deficiency of tunnel number, Math. Ann. 317 (2000), 783-820.
  61. (With H. Goda and A. Thompson) Levelling an unknotting tunnel, Geometry & Topology 4 (2000) 243-275
  62. (coedited with Joel Hass) Proceedings of the 1998 Kirbyfest, Geometry and Topology Monographs 2 (1999).
  63. (With A. Thompson) Unknotting tunnels and Seifert surfaces, Proc. London Math. Soc. 87 (2003) 523--544
  64. Heegaard reducing spheres for the 3-sphere , Rend. Istit. Mat. Univ. Trieste 32 (2001) 397--410.
  65. There are no unexpected tunnel number one knots of genus one , Trans. AMS. 356 (2004) 1385-1442.
  66. The Goda-Teragaito Conjecture: an overview Proceedings of the 2001 RIMS Conference on Heegaard Splittings and Dehn surgeries of 3-manifolds, Surikaisekikenkyusho Kokyuroku 1229 (2002) 87-102.
  67. (With A. Thompson) Thinning genus two Heegaard spines in S3, Knot theory and its Ramifications 12 (2003) 683-708.
  68. (notes by Ruifeng Qiu) Heegaard splittings of 3-manifolds, Low dimensional topology: lectures at the Morningside Center of Mathematics, ed. Benghe Li, Shicheng Wang, Xuezhi Zhao, 25--39, International Press, 2003.
  69. (With J. Schultens) 3-manifolds with planar presentations and the width of satellite knots , Transactions of the AMS 358 (2006), 3781--3805.
  70. Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting , Bol. Soc. Mat. Mexicana 10 (2004), Special Issue, 503--514.
  71. (with A. Thompson) Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds, Proc. Amer. Math. Soc. 133 (2005) 1573--1580.
  72. Thin position in the theory of classical knots, Handbook of Knot theory, ed. William W. Menasco and Morwen B. Thistlethwaite, 429--459, North-Holland, Amsterdam, 2005.
  73. (with A. Thompson) On the additivity of knot width, in Proceedings of the Casson Fest, Geometry and Topology Monographs 7 (2004) 135-144.
  74. Proximity in the curve complex: boundary reduction and bicompressible surfaces , Pacific J. Math. 228 (2006) 325--348
  75. (with M. Tomova) Alternate Heegaard genus bounds distance , Geometry and Topology 10 (2006) 593--617.
  76. (with T. Saito and J. Schultens) Lecture notes on generalized Heegaard splittings, ArXiv preprint math.GT/0504167
  77. Generalized Property R and the Schoenflies Conjecture, Commentarii Mathematici Helvetici, 83 (2008) 421--449.
  78. Refilling meridians in a genus 2 handlebody complement, in The Zieschang Gedenkschrift, Geometry and Topology Monographs 14 (2008) 451--475 .
  79. (with M. Tomova) Conway products and links with multiple bridge surfaces, Mich. Math. Jour. 56 (2008) 113--144.
  80. (with M. Tomova) Uniqueness of bridge surfaces for 2-bridge knots, Math. Proc. Cambridge Phil. Soc. 144 (2008) 639--650.
  81. (with R. Qiu) A proof of the Gordon Conjecture, Advances in Mathematics 22 (2009) 2085--2106.
  82. (coedited with Michel Boileau and Richard Weidmann) The Zieschang Gedenkschrift, Geometry and Topology Monographs 14 (2008).
  83. (With A. Thompson) Surgery on a knot in (Surface x I), Algebraic and Geometric Topology 9 (2009) 1825--1835.
  84. Much of following work summarized in: An overview of Property 2R, Proceedings of the Heidelberg Knot Theory Semester, ed. by Markus Banagl and Denis Vogel, Springer (2011) 317-325.
    1. (With A. Thompson) Fibered knots and Property 2R, ArXiv preprint math.0901.2319
    2. (With R. Gompf) Fibered knots and Property 2R, II, ArXiv preprint arXiv:0908.2795
    3. (with R. Gompf and A. Thompson; combines and augments the previous two items) Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures, Geometry and Topology 14 (2010) 2305-2347.

  85. (With J. Berge) Multiple genus 2 Heegaard splittings: a missed case, Algebraic and Geometric Topology 11 (2011) 1781-1792.
  86. Berge's distance 3 pairs of genus 2 Heegaard splittings Math. Pro. Camb. Phil. Soc. 151 (2011) 293-306.
  87. (coedited with C. Hodgson, W. Jaco, and S. Tillmann) Geometry and Topology Down Under American Mathematical Society, Contemporary Math 597 (2013).

  88. Generating the genus g+1 Goeritz group of a genus g handlebody, in Geometry and Topology Down Under, ed. by C. Hodgson, W. Jaco, M. Scharlemann, and S. Tillmann, American Mathematical Society, Contemporary Math 597 (2013) 347-369.

  89. Proposed Property 2R counterexamples classified, Ill. Jour. Math., 60 (2016) 207-250.

  90. (with Toshio Saito and Jennifer Schultens) Lectures Notes on Generalized Heegaard Splittings World Scientific (2016).

  91. (with Michael Freedman) Dehn's lemma for immersed loops, ArXiv preprint arXiv:1704.05507

A preprint accessible above may differ somewhat from its final published version.