The topic of this book is 3-manifold groups, that is, fundamental groups of compact 3-
manifolds. This class of groups sits between the class of fundamental groups of surfaces …

An oriented three-manifold with torus boundary admits either no L-space Dehn filling, a
unique L-space filling, or an interval of L-space fillings. In the latter case, which we call …

We prove for the first time that knot Floer homology and Khovanov homology can detect non-
fibered knots and that HOMFLY homology detects infinitely many knots; these theories were …

It has been a central open problem in Heegaard Floer theory whether cobordisms of links
induce homomorphisms on the associated link Floer homology groups. We provide an …

We propose a nonperturbative construction of Hopf algebras that represent categories of
line operators in topological quantum field theory, in terms of semi-extended operators …

arxiv:1205.0202v3 [math.GT] 24 Apr 2013 Page 1 arxiv:1205.0202v3 [math.GT] 24 Apr 2013
3-MANIFOLD GROUPS MATTHIAS ASCHENBRENNER, STEFAN FRIEDL, AND HENRY …

This is a companion paper to earlier work of the authors, which interprets the Heegaard
Floer homology for a manifold with torus boundary in terms of immersed curves in a …

In this paper, we extend the theory of sutured Floer homology developed by the author. We
first prove an adjunction inequality and then define a polytope P (M, γ) in H 2 (M,∂ M; ℝ) that …

We give an explicit construction of the Honda–Kazez–Matić gluing maps in terms of contact
handles. We use this to prove a duality result for turning a sutured manifold cobordism …

We define a link lattice complex for plumbed links, generalizing constructions of Ozsváth,
Stipsicz and Szabó, and of Gorsky and Némethi. We prove that for all plumbed links in …