Publications  Martin Scharlemann
Math
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A preprint accessible below may differ somewhat from its final published
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(With R. Kirby) A curious category which equals TOP. Manifolds
Tokyo1973: Proceedings of the 1973 Tokyo conference on the topology
of
manifolds, University of Tokyo, 1975, 9397.

(With L. Siebenmann) The Hauptvermutung for smooth singular
homeomorphisms.
ManifoldsTokyo1973: Proceedings of the 1973 Tokyo conference on
the
topology of manifolds, University of Tokyo, 1975, 8591.

(With L. Siebenmann) The Hauptvermutung for smooth homeomorphisms
II:
A proof valid for open 4manifolds. Compositio Math. 29
(1974)
253263.

Equivalence of 5dimensional scobordisms. Proc. AMS 53
(1975)
508510.

Simplicial Triangulation of noncombinatorial manifolds of dimension less than
nine. Trans. Am. Math. Soc. 219 1 (1976) 269287.

Constructing strange manifolds with the dodecahedral space.
Duke
Math. J. 43 (1976) 3340.

Transversality theories at dimension 4. Inventiones Math.
33
(1976) 114.
 (With R. C. Kirby) Eight faces of the Poincare homology 3sphere
in Geometric Topology ed. by James C. Cantrell, Academic Press, 1979,
pp. 113146.

Thoroughly knotted homology spheres. Houston J. Math. 3
(1977)
271283.

The fundamental group of fibered knot cobordisms. Math. Ann.
225
(1977) 243251.

Isotopy and cobordism of homology spheres in spheres. J. London
Math. Soc. 16 (1977) 559567.

NonPL imbeddings of 3manifolds. Amer. J. Math. 100
(1978)
539546.

Approximating CAT CE maps by CAT homeomorphisms. in Geometric
Topology
ed. by James C. Cantrell, Academic Press, 1979, pp. 475501.

Smooth CE maps and smooth homeomorphisms. in Algebraic and
Geometric
Topology, ed. by Kenneth Millett, Lecture notes in Mathematics #664,
Springer,
1978, pp. 234240.

Transverse Whitehead triangulations. Pacific J. Math. 80
(1979) 245251.

Subgroups of SL(2,R) freely generated by three parabolic elements
Linear
and Multilinear Algebra 7 (1979) 177191.

Essential tori in 4manifold boundaries. Pacific J. Math.
105
(1983) 439447.

The subgroup of Δ_{2} generated by torus automorphisms. Math.
Ann.
251 (1980) 263268.

The complex of curves on nonorientable surfaces. J. London
Math.
Soc. 25 (1982) 171184.

(With Craig Squier) Automorphisms of the free group of rank two
without
finite orbits. AMS Contemporary Mathematics Series 20
(1983)
341346.

Tunnel number one knots satisfy the Poenaru conjecture.
Topology
and its Applications. 18 (1984) 235258.

The fourdimensional Schoenflies conjecture is true for genus two
imbeddings.
Topology 23 (1984) 211217.

Outermost forks and a theorem of Jaco. AMS Contemp. Math.
44
(1985) 189193.

3manifolds with H_{2}(A, ∂A) = 0 and a conjecture of Stallings.
in Knot theory and manifolds, Lecture notes in Math. #1144,
Springer,
1985, pp. 138145.

Smooth Spheres in R^{4} with four critical points are standard.
Inventiones
Math. 79 (1985) 125141.

Unknotting number one knots are prime. Inventiones Math.
82
(1985) 3755.

(With S. Bleiler) Tangles, Property P and a problem of J. Martin
Math.
Ann. 273 14 (1986) 215255.

The Thurston norm and 2handle addition. Proc. Am. Math. Soc.
100
(1987) 362366.

(With S. Bleiler) A projective plane in R^{4} with three critical
points
is standard. Topology 27 (1988) 519540.

A remark on companionship and property P. Proc. Am. Math. Soc.
98
(1986) 169170.

Sutured manifolds and generalized Thurston norms, Jour. Diff.
Geometry,
29 (1989) 557614.

(With A. Thompson) Unknotting number, genus, and companion tori.
Math.
Ann. 280 (1988) 191205.

(With A. Thompson) Finding disjoint Seifert surfaces Bull. Lon.
Math. Soc. 20 (1988) 6164.

(With A. Thompson) Link genus and the Conway moves. Commentarii
Math.
Helvetici 64 (1989) 527535.

Producing reducible 3manifolds by surgery on a knot.
Topology
29 (1990) 481500.

(With A. Thompson) Detecting unknotted graphs in 3space .
Jour.
Diff. Geom. 34 (1991) 539560.

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, 2950.

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, 351354.

Handlebody complements in the 3sphere: A remark on a theorem of
Fox.
Proc. Amer. Math. Soc. 115(1992) 11151117.

Unknotting via simultaneous crossing changes. Trans. Amer.
Math.
Soc. 336 (1993) 855868.

Lectures on the theory of sutured manifolds. in Korea Advanced
Inst.
of Technology Workshop Proceedings, 1990, pp. 2546.

(With A. Thompson) Heegaard splittings of (surface) x I are
standard.
Math. Ann. 295 (1993) 549564.

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. 6582.

(With Y. Q. Wu) Hyperbolic manifolds and degenerating handle
additions.
J. Austral. Math. Soc. 55 (1993) 7289.

(With A. Thompson) Pushing arcs and graphs around in handlebodies
in
Proceedings of the Knoxville lowdimensional topology conference,
International
Press, 1994, 163171.

(With A. Thompson) Thin position and Heegaard splittings of the 3
sphere.
Jour. Diff. Geom. 39 (1994) 343357.

(With A. Thompson) Thin position for 3manifolds. AMS
Contemporary
Math. 164 (1994) 231238.
 (With H. Rubinstein) Comparing
Heegaard splittings of nonHaken 3 manifolds. Topology, 35
(1996) 10051026.

(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) 6983.

(With H. Rubinstein) Comparing Heegaard splittings
 the bounded case . Trans. AMS, 350 (1998)
689715.

Local detection of strongly irreducible Heegaard splittings,
Topology and its Applications. 90 (1998) 135147.
 Heegaard
splittings of compact 3manifolds, Handbook of geometric topology,
ed by R. Daverman and R. Sherr, 921953, NorthHolland, Amsterdam, 2002.
 Crossing Changes, Chaos, Solitons,
and Fractals, 9 (1998) 693704.
 (With H. Rubinstein) Genus two
Heegaard splittings of orientable 3manifolds Proceedings of the
1998 Kirbyfest, Geometry
and Topology Monographs 2 (1999) 489553.

(With J. Schultens) The tunnel
number of the connect sum of n knots
is at least n, Topology 38 (1999) 265270.

(With J. Schultens) Comparing
Heegaard and JSJ structures of orientable
3manifolds, Trans. Amer. Math. Soc.
353 (2001) 557584.

(With D. Cooper) The structure of
a solvmanifold's Heegaard splittings,
Proceedings of the Gökova GeometryTopology Conference 1998
(also
in Turkish Journal of Mathematics 23 (1999)) 118.

(With M. Jones) How a strongly
irreducible Heegaard splitting intersects a handlebody,
Topology and its Applications 110 (2001) 289301

(With J. Schultens) Annuli in
generalized Heegaard splittings and deficiency
of tunnel number, Math. Ann. 317 (2000), 783820.

(With H. Goda and A. Thompson) Levelling
an unknotting tunnel, Geometry & Topology 4 (2000)
243275

(coedited with Joel Hass) Proceedings
of the 1998 Kirbyfest, Geometry and Topology Monographs
2
(1999).

(With A. Thompson)
Unknotting tunnels and Seifert surfaces,
Proc. London Math. Soc. 87 (2003) 523544
 Heegaard reducing spheres for the 3sphere
, Rend. Istit. Mat. Univ. Trieste 32 (2001) 397410.

There are no unexpected tunnel number one knots of genus one
, Trans. AMS. 356 (2004) 13851442.

The GodaTeragaito Conjecture: an overview
Proceedings of the 2001 RIMS Conference on Heegaard Splittings and
Dehn surgeries of 3manifolds, Surikaisekikenkyusho Kokyuroku
1229 (2002) 87102.
 (With A. Thompson) Thinning genus two
Heegaard spines in S^{3}, Knot theory and its Ramifications
12 (2003) 683708.
 (notes by Ruifeng Qiu) Heegaard splittings of 3manifolds, Low dimensional topology: lectures at the Morningside Center of Mathematics, ed. Benghe Li, Shicheng Wang, Xuezhi Zhao, 2539, International Press, 2003.
 (With J. Schultens) 3manifolds with
planar presentations and the width of satellite knots , Transactions of the AMS
358 (2006), 37813805.
 Automorphisms of the 3sphere that
preserve a genus two Heegaard splitting , Bol. Soc. Mat. Mexicana 10 (2004), Special Issue, 503514.
 (with A. Thompson) Surfaces,
submanifolds, and aligned Fox reimbedding in nonHaken 3manifolds, Proc. Amer. Math. Soc. 133 (2005) 15731580.
 Thin position in the theory of classical knots, Handbook of Knot theory, ed. William W. Menasco and
Morwen B. Thistlethwaite, 429459, NorthHolland, Amsterdam, 2005.
 (with A. Thompson) On the
additivity of knot width, in Proceedings of the Casson Fest, Geometry and Topology
Monographs 7 (2004) 135144.
 Proximity in the curve complex:
boundary reduction and bicompressible surfaces , Pacific J. Math. 228 (2006) 325348
 (with M. Tomova) Alternate Heegaard
genus bounds distance , Geometry and Topology 10 (2006) 593617.
 (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) 421449.
 Refilling meridians in a genus 2 handlebody complement, in The Zieschang Gedenkschrift, Geometry and Topology Monographs
14
(2008) 451475 .
 (with M. Tomova) Conway products and links with multiple bridge surfaces, Mich. Math. Jour. 56 (2008) 113144.
 (with M. Tomova) Uniqueness of bridge surfaces for 2bridge knots, Math. Proc. Cambridge Phil. Soc. 144 (2008) 639650.
 (with R. Qiu) A proof of the Gordon Conjecture, Advances in Mathematics 22 (2009) 20852106.

(coedited with Michel Boileau and Richard Weidmann) The Zieschang Gedenkschrift, Geometry and Topology Monographs
14
(2008).

(With A. Thompson) Surgery on a knot in (Surface x I), Algebraic and Geometric Topology 9 (2009) 18251835.
 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) 317325.

(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 SliceRibbon Conjectures, Geometry and Topology 14 (2010) 23052347.

(With J. Berge) Multiple genus 2 Heegaard splittings: a missed case, Algebraic and Geometric Topology 11 (2011) 17811792.

Berge's distance 3 pairs of genus 2 Heegaard splittings Math. Pro. Camb. Phil. Soc. 151 (2011) 293306.

(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) 347369.

Proposed Property 2R counterexamples classified, Ill. Jour. Math., 60 (2016) 207250.

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

(with Michael Freedman) Dehn's lemma for immersed loops,
Math. Res. Lett. 25 (2018), no. 6, 18271836.
ArXiv preprint arXiv:1704.05507

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

One Powell generator is redundant,
ArXiv preprint arXiv:1908.00479

A strong Haken's Theorem,
ArXiv preprint arXiv:2003.08523

(with Michael Freedman) Uniqueness in Haken's Theorem,
ArXiv preprint arXiv:2004.07385, to appear in Michigan Mathematical Journal

Generating the Goeritz group,
ArXiv preprint arXiv:2011.10613
A preprint accessible above may differ somewhat from its final published
version.