Surgery and involutions on 4-manifolds

We prove that the canonical 4-dimensional surgery problems can be solved after passing to a double cover. This contrasts the long-standing conjecture about the validity of the topological surgery theorem for arbitrary fundamental groups (without passing to a cover). As a corollary, the surgery conjecture is reformulated in terms of the existence of free involutions on a certain class of 4-manifolds. We consider this question and analyze its relation to the A,B-slice problem.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-70.abs.htm

Exponential separation in 4-manifolds

We use a new geometric construction, grope splitting, to give a sharp bound for separation of surfaces in 4-manifolds. We also describe applications of this technique in link-homotopy theory, and to the problem of locating pi_1-null surfaces in 4-manifolds. In our applications to link-homotopy, grope splitting serves as a geometric substitute for the Milnor group.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper13.abs.htm

Subexponential groups in 4-manifold topology

We present a new, more elementary proof of the Freedman-Teichner result that the geometric classification techniques (surgery, s-cobordism, and pseudoisotopy) hold for topological 4-manifolds with groups of subexponential growth. In an appendix Freedman and Teichner give a correction to their original proof, and reformulate the growth estimates in terms of coarse geometry.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper14.abs.htm

The Holography of F-maximization

We find new supersymmetric backgrounds of ${\cal N} = 8$ gauged supergravity in four Euclidean dimensions that are dual to deformations of ABJM theory on $S^3$. The deformations encode the most general choice of $U(1)_R$ symmetry used to define the theory on $S^3$. We work within an ${\cal N} = 2$ truncation of the ${\cal N} = 8$ supergravity theory obtained via a group theory argument. We find perfect agreement between the $S^3$ free energy computed from our supergravity backgrounds and the previous field theory computations of the same quantity based on supersymmetric localization and matrix model techniques.Comment: 48 pages; v2 minor improvement

Alexander duality, gropes and link homotopy

We prove a geometric refinement of Alexander duality for certain 2-complexes, the so-called gropes, embedded into 4-space. This refinement can be roughly formulated as saying that 4-dimensional Alexander duality preserves the disjoint Dwyer filtration. In addition, we give new proofs and extended versions of two lemmas of Freedman and Lin which are of central importance in the A-B-slice problem, the main open problem in the classification theory of topological 4-manifolds. Our methods are group theoretical, rather than using Massey products and Milnor \mu-invariants as in the original proofs.Comment: 19 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper5.abs.htm

Histone H1 is essential for mitotic chromosome architecture and segregation in Xenopus laevis egg extracts.

During cell division, condensation and resolution of chromosome arms and the assembly of a functional kinetochore at the centromere of each sister chromatid are essential steps for accurate segregation of the genome by the mitotic spindle, yet the contribution of individual chromatin proteins to these processes is poorly understood. We have investigated the role of embryonic linker histone H1 during mitosis in Xenopus laevis egg extracts. Immunodepletion of histone H1 caused the assembly of aberrant elongated chromosomes that extended off the metaphase plate and outside the perimeter of the spindle. Although functional kinetochores assembled, aligned, and exhibited poleward movement, long and tangled chromosome arms could not be segregated in anaphase. Histone H1 depletion did not significantly affect the recruitment of known structural or functional chromosomal components such as condensins or chromokinesins, suggesting that the loss of H1 affects chromosome architecture directly. Thus, our results indicate that linker histone H1 plays an important role in the structure and function of vertebrate chromosomes in mitosis