Contact handles, duality, and sutured Floer homology

We give an explicit construction of the Honda--Kazez--Mati\'c gluing maps in terms of contact handles. We use this to prove a duality result for turning a sutured manifold cobordism around, and to compute the trace in the sutured Floer TQFT. We also show that the decorated link cobordism maps on the hat version of link Floer homology defined by the first author via sutured manifold cobordisms and by the second author via elementary cobordisms agree.Comment: 86 pages, 54 figures, to appear in Geometry and Topolog

Knot cobordisms, bridge index, and torsion in Floer homology

Given a connected cobordism between two knots in the 3-sphere, our main result is an inequality involving torsion orders of the knot Floer homology of the knots, and the number of local maxima and the genus of the cobordism. This has several topological applications: The torsion order gives lower bounds on the bridge index and the band-unlinking number of a knot, the fusion number of a ribbon knot, and the number of minima appearing in a slice disk of a knot. It also gives a lower bound on the number of bands appearing in a ribbon concordance between two knots. Our bounds on the bridge index and fusion number are sharp for $T_{p,q}$ and $T_{p,q}\# \overline{T}_{p,q}$, respectively. We also show that the bridge index of $T_{p,q}$ is minimal within its concordance class. The torsion order bounds a refinement of the cobordism distance on knots, which is a metric. As a special case, we can bound the number of band moves required to get from one knot to the other. We show knot Floer homology also gives a lower bound on Sarkar's ribbon distance, and exhibit examples of ribbon knots with arbitrarily large ribbon distance from the unknot.Comment: 21 pages, 7 figures, to appear in the Journal of Topolog

John Miles Foley, How to read an oral poem, Urbana and Chicago, University of Illinois Press, 2002, 256 pp. ISBN 978-0-252-07082-8

This title leads the reader directly to the book’s main business: imparting useful strategies for reading records of verbal arts. It contemplates the dimensions of performance endemic to them, why it is important to account for those aspects when reading, and how performance itself enmeshes verbal expressions in social fabric, both past and present. The primary audience for the book is the general reader. It offers a straightforward exposition of fundamental insights into the nature and function of verbal arts, based on the collective achievements of modern scholarship in the field, and, especially, on summaries of the author’s pioneering work in Homeric Greek, Old English, and modern South Slavic traditions