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, Math. Res. Lett. 25 (2018), no. 6, 1827-1836. ArXiv preprint arXiv:1704.05507

  92. (with Michael Freedman) Powell moves and the Goeritz group, ArXiv preprint arXiv:1804.05909

  93. One Powell generator is redundant, Proc. Amer. Math. Soc. Ser. B 7 (2020), 138-141. ArXiv preprint arXiv:1908.00479

  94. A strong Haken's Theorem, ArXiv preprint arXiv:2003.08523 , to appear in Algebraic and Geometric Topology

  95. (with Michael Freedman) Uniqueness in Haken's Theorem, Michigan Math. J. 74 (2024) 119-142. ArXiv preprint arXiv:2004.07385

  96. Generating the Goeritz group of S3, ArXiv preprint arXiv:2011.10613 , to appear in Jour. Assoc. Math. Res.

  97. Powell's Conjecture on the Goeritz group of the 3-sphere is stably true, ArXiv preprint arXiv:2210.13629, to appear in Algebraic and Geometric Topology

Minor non-math writings

  1. Commencement address, UCSB Science and Mathematics (1984).

  2. A tribute to Abby Thompson for her 60th birthday celebration, (2018).

  3. Scharlemanns in Bochum (2021).

  4. Rob Kirby comes to Berkeley, in Robion C. Kirby volume of Celebratio Mathematica (2022).

  5. A paragraph on Dennis Sullivan *66 in Princeton Alumni Weekly (2022).

  6. Remembering Barbara Hoyer, the jonestown report 25 (2023).

  7. A tribute to Mario Eudave-Muñoz for his 60th birthday celebration, (2023).