Publications - Martin Scharlemann
Reviews of these papers (requires MathSciNet
A preprint accessible below may differ somewhat from its final published
(With R. Kirby) A curious category which equals TOP. Manifolds-
Tokyo-1973: Proceedings of the 1973 Tokyo conference on the topology
manifolds, University of Tokyo, 1975, 93-97.
(With L. Siebenmann) The Hauptvermutung for smooth singular
Manifolds-Tokyo-1973: Proceedings of the 1973 Tokyo conference on
topology of manifolds, University of Tokyo, 1975, 85-91.
(With L. Siebenmann) The Hauptvermutung for smooth homeomorphisms
A proof valid for open 4-manifolds. Compositio Math. 29
Equivalence of 5-dimensional s-cobordisms. Proc. AMS 53
Simplicial Triangulation of non-combinatorial manifolds of dimension less than
nine. Trans. Am. Math. Soc. 219 1 (1976) 269-287.
Constructing strange manifolds with the dodecahedral space.
Math. J. 43 (1976) 33-40.
Transversality theories at dimension 4. Inventiones Math.
- (With R. C. Kirby) Eight faces of the Poincare homology 3-sphere
in Geometric Topology ed. by James C. Cantrell, Academic Press, 1979,
Thoroughly knotted homology spheres. Houston J. Math. 3
The fundamental group of fibered knot cobordisms. Math. Ann.
Isotopy and cobordism of homology spheres in spheres. J. London
Math. Soc. 16 (1977) 559-567.
Non-PL imbeddings of 3-manifolds. Amer. J. Math. 100
Approximating CAT CE maps by CAT homeomorphisms. in Geometric
ed. by James C. Cantrell, Academic Press, 1979, pp. 475-501.
Smooth CE maps and smooth homeomorphisms. in Algebraic and
Topology, ed. by Kenneth Millett, Lecture notes in Mathematics #664,
1978, pp. 234-240.
Transverse Whitehead triangulations. Pacific J. Math. 80
Subgroups of SL(2,R) freely generated by three parabolic elements
and Multilinear Algebra 7 (1979) 177-191.
Essential tori in 4-manifold boundaries. Pacific J. Math.
The subgroup of Δ2 generated by torus automorphisms. Math.
251 (1980) 263-268.
The complex of curves on non-orientable surfaces. J. London
Soc. 25 (1982) 171-184.
(With Craig Squier) Automorphisms of the free group of rank two
finite orbits. AMS Contemporary Mathematics Series 20
Tunnel number one knots satisfy the Poenaru conjecture.
and its Applications. 18 (1984) 235-258.
The four-dimensional Schoenflies conjecture is true for genus two
Topology 23 (1984) 211-217.
Outermost forks and a theorem of Jaco. AMS Contemp. Math.
3-manifolds with H2(A, ∂A) = 0 and a conjecture of Stallings.
in Knot theory and manifolds, Lecture notes in Math. #1144,
1985, pp. 138-145.
Smooth Spheres in R4 with four critical points are standard.
Math. 79 (1985) 125-141.
Unknotting number one knots are prime. Inventiones Math.
(With S. Bleiler) Tangles, Property P and a problem of J. Martin
Ann. 273 14 (1986) 215-255.
The Thurston norm and 2-handle addition. Proc. Am. Math. Soc.
(With S. Bleiler) A projective plane in R4 with three critical
is standard. Topology 27 (1988) 519-540.
A remark on companionship and property P. Proc. Am. Math. Soc.
Sutured manifolds and generalized Thurston norms, Jour. Diff.
29 (1989) 557-614.
(With A. Thompson) Unknotting number, genus, and companion tori.
Ann. 280 (1988) 191-205.
(With A. Thompson) Finding disjoint Seifert surfaces Bull. Lon.
Math. Soc. 20 (1988) 61-64.
(With A. Thompson) Link genus and the Conway moves. Commentarii
Helvetici 64 (1989) 527-535.
Producing reducible 3-manifolds by surgery on a knot.
29 (1990) 481-500.
(With A. Thompson) Detecting unknotted graphs in 3-space .
Diff. Geom. 34 (1991) 539-560.
Planar graphs, family trees, and braids. in Progress in Knot
and related Topics, M. Boileau, M. Domergue, Y. Mathieu & K.
eds., Hermann, 1997, 29-50.
Some pictorial remarks on Suzuki's Brunnian graph. in Topology
- Proc. of Ohio State Topology Year, B. Apanasov, W. D. Neumann, A. W.
Reid and L. Siebenmann, eds., Walter de Gruyter, 1992, 351-354.
Handlebody complements in the 3-sphere: A remark on a theorem of
Proc. Amer. Math. Soc. 115(1992) 1115-1117.
Unknotting via simultaneous crossing changes. Trans. Amer.
Soc. 336 (1993) 855-868.
Lectures on the theory of sutured manifolds. in Korea Advanced
of Technology Workshop Proceedings, 1990, pp. 25-46.
(With A. Thompson) Heegaard splittings of (surface) x I are
Math. Ann. 295 (1993) 549-564.
Topology of knots. in Topological Aspects of the Dynamics of
and Plasmas, H. K. Moffatt, G. M. Zaslavsky, P. Comte, M. Tabor, eds.,
Kluwer Academic Publishers, 1992, pp. 65-82.
(With Y. Q. Wu) Hyperbolic manifolds and degenerating handle
J. Austral. Math. Soc. 55 (1993) 72-89.
(With A. Thompson) Pushing arcs and graphs around in handlebodies
Proceedings of the Knoxville low-dimensional topology conference,
Press, 1994, 163-171.
(With A. Thompson) Thin position and Heegaard splittings of the 3-
Jour. Diff. Geom. 39 (1994) 343-357.
(With A. Thompson) Thin position for 3-manifolds. AMS
Math. 164 (1994) 231-238.
(With H. Rubinstein) Comparing
Heegaard splittings of non-Haken 3- manifolds. Topology, 35
(With Anneke Bart) Least weight injective surfaces are fundamental.
Topology & its Applications 69 (1995) 251- 264.
(With H. Rubinstein) Transverse Heegaard splittings. Mich. Math
Jour. 44 (1997) 69-83.
(With H. Rubinstein) Comparing Heegaard splittings
- the bounded case . Trans. AMS, 350 (1998)
Local detection of strongly irreducible Heegaard splittings,
Topology and its Applications. 90 (1998) 135-147.
splittings of compact 3-manifolds, Handbook of geometric topology,
ed by R. Daverman and R. Sherr, 921--953, North-Holland, Amsterdam, 2002.
Crossing Changes, Chaos, Solitons,
and Fractals, 9 (1998) 693-704.
(With H. Rubinstein) Genus two
Heegaard splittings of orientable 3-manifolds Proceedings of the
1998 Kirbyfest, Geometry
and Topology Monographs 2 (1999) 489-553.
(With J. Schultens) The tunnel
number of the connect sum of n knots
is at least n, Topology 38 (1999) 265-270.
(With J. Schultens) Comparing
Heegaard and JSJ structures of orientable
3-manifolds, Trans. Amer. Math. Soc.
353 (2001) 557-584.
(With D. Cooper) The structure of
a solvmanifold's Heegaard splittings,
Proceedings of the Gökova Geometry-Topology Conference 1998
in Turkish Journal of Mathematics 23 (1999)) 1-18.
(With M. Jones) How a strongly
irreducible Heegaard splitting intersects a handlebody,
Topology and its Applications 110 (2001) 289-301
(With J. Schultens) Annuli in
generalized Heegaard splittings and deficiency
of tunnel number, Math. Ann. 317 (2000), 783-820.
(With H. Goda and A. Thompson) Levelling
an unknotting tunnel, Geometry & Topology 4 (2000)
(coedited with Joel Hass) Proceedings
of the 1998 Kirbyfest, Geometry and Topology Monographs
(With A. Thompson)
Unknotting tunnels and Seifert surfaces,
Proc. London Math. Soc. 87 (2003) 523--544
Heegaard reducing spheres for the 3-sphere
, Rend. Istit. Mat. Univ. Trieste 32 (2001) 397--410.
There are no unexpected tunnel number one knots of genus one
, Trans. AMS. 356 (2004) 1385-1442.
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.
(With A. Thompson) Thinning genus two
Heegaard spines in S3, Knot theory and its Ramifications
12 (2003) 683-708.
(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.
(With J. Schultens) 3-manifolds with
planar presentations and the width of satellite knots , Transactions of the AMS
358 (2006), 3781--3805.
Automorphisms of the 3-sphere that
preserve a genus two Heegaard splitting , Bol. Soc. Mat. Mexicana 10 (2004), Special Issue, 503--514.
(with A. Thompson) Surfaces,
submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds, Proc. Amer. Math. Soc. 133 (2005) 1573--1580.
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.
(with A. Thompson) On the
additivity of knot width, in Proceedings of the Casson Fest, Geometry and Topology
Monographs 7 (2004) 135-144.
Proximity in the curve complex:
boundary reduction and bicompressible surfaces , Pacific J. Math. 228 (2006) 325--348
(with M. Tomova) Alternate Heegaard
genus bounds distance , Geometry and Topology 10 (2006) 593--617.
(with T. Saito and J. Schultens) Lecture notes
on generalized Heegaard splittings, ArXiv preprint math.GT/0504167
Generalized Property R and the Schoenflies Conjecture, Commentarii Mathematici Helvetici, 83 (2008) 421--449.
Refilling meridians in a genus 2 handlebody complement, in The Zieschang Gedenkschrift, Geometry and Topology Monographs
(2008) 451--475 .
(with M. Tomova) Conway products and links with multiple bridge surfaces, Mich. Math. Jour. 56 (2008) 113--144.
(with M. Tomova) Uniqueness of bridge surfaces for 2-bridge knots, Math. Proc. Cambridge Phil. Soc. 144 (2008) 639--650.
(with R. Qiu) A proof of the Gordon Conjecture, Advances in Mathematics 22 (2009) 2085--2106.
(coedited with Michel Boileau and Richard Weidmann) The Zieschang Gedenkschrift, Geometry and Topology Monographs
(With A. Thompson) Surgery on a knot in (Surface x I), Algebraic and Geometric Topology 9 (2009) 1825--1835.
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.
(With A. Thompson) Fibered knots and Property 2R, ArXiv preprint math.0901.2319
(With R. Gompf) Fibered knots and Property 2R, II, ArXiv preprint arXiv:0908.2795
(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.
(With J. Berge) Multiple genus 2 Heegaard splittings: a missed case, Algebraic and Geometric Topology 11 (2011) 1781-1792.
Berge's distance 3 pairs of genus 2 Heegaard splittings Math. Pro. Camb. Phil. Soc. 151 (2011) 293-306.
(coedited with C. Hodgson, W. Jaco, and S. Tillmann) Geometry and Topology Down Under American Mathematical Society, Contemporary Math 597 (2013).
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.
Proposed Property 2R counterexamples classified, Ill. Jour. Math., 60 (2016) 207-250.
(with Toshio Saito and Jennifer Schultens) Lectures Notes on Generalized Heegaard Splittings World Scientific (2016).
(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