Publications and Preprints

Surface complexes of Seifert fibered spaces

Kakimizu complexes of Seifert fibered spaces

The Kakimizu complex of a surface

Contractibility of the Kakimizu complex and symmetric Seifert surfaces, with Piotr Przytycki

Width complexes of knots and 3-manifolds

The Kakimizu complex is simply connected

Destabilizing amalgamated Heegaard splittings , with Richard Weidmann

Bridge numbers of torus knots

Thin position of knots and 3-manifolds , with Hugh Howards

Thin position of knots and 3-manifolds: A unified approach , with Hugh Howards, Yo'av Rieck

On the geometric and algebraic rank of graph manifolds , with Richard Weidmann

Heegaard genus formula for Haken manifolds

3-manifolds with planar presentations and the width of satellite knots , with Marty Scharlemann

Heegaard splittings of graph manifolds

Additivity of Bridge Numbers of Knots

Genus 2 hyperbolic 3-manifolds of arbitrarily large volume

Comparing Heegaard and JSJ structures or orientable 3-manifolds , with Marty Scharlemann

Annuli in generalized Heegaard splittings and degeneration of tunnel number , with Marty Scharlemann

The tunnel number of the sum of n knots is at least n , with Marty Scharlemann

Tunnel numbers of small knots do not go down under connected sum , with Kanji Morimoto

Additivity of tunnel number for small knots

The stabilization problem for Heegaard splittings of Seifert fibered spaces

Weakly reducible Heegaard splittings of Seifert fibered spaces

Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal , with Yoav Moriah

Heegaard splittings of Seifert fibered spaces with boundary

The classification of Heegaard splittings for (compact orientable surface) x circle

Here are a few older manuscripts that are educational. I don't currently intend to publish these, for a variety of reasons. Of course, I could change my mind.

Waldhausen's "Heegaardzerlegungen der 3-Sphaere"

(This is an annotated and illustrated translation, written for the benefit of local graduate students. I recently noticed that S. Schleimer has something along these lines as well.)

Amalgamations of Heegaard splittings are unique

(This is addressed elsewhere, for instance by D. Bachman and M. Lackenby. The result seems kind of obvious, but there is an issue here.)

Below is a very coarse set of notes that I compiled for a course on 3-manifolds. Much of my lecturing time was spent drawing appropriate pictures. I hope to substantially revise these notes and add the pictures sometime in the future.

Sketchy notes for a class on 3-manifolds

If you have any questions or comments, send mail to jcs at math dot ucdavis dot edu.