Related papers: Intersection pairing on hyperbolic 4-manifolds

We calculate intersection forms of all 4-dimensional almost-flat manifolds

Given a diagram for a trisection of a 4-manifold $X$, we describe the homology and the intersection form of $X$ in terms of the three subgroups of $H_1(\Sigma;\mathbb{Z})$ generated by the three sets of curves and the intersection pairing…

We study the relationship between two norms on the first cohomology of a hyperbolic 3-manifold: the purely topological Thurston norm and the more geometric harmonic norm. Refining recent results of Bergeron, \c{S}eng\"un, and Venkatesh as…

We derive an obstruction to representing a homology class of a symplectic 4-manifold by an embedded, possibly disconnected, symplectic surface.

A multisection of a 4-manifold is a decomposition into 1-handlebodies intersecting pairwise along 3-dimensional handlebodies or along a central closed surface; this generalizes the Gay-Kirby trisections. We show how to compute the twisted…

For a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of $M$. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont, and…

We study the intersection theory of punctured pseudoholomorphic curves in $4$-dimensional symplectic cobordisms. We first study the local intersection properties of such curves at the punctures. We then use this to develop topological…

In this paper we shall give formulas for the pairings of intersection cohomology classes of complementary dimensions in the intersection cohomology of geometric invariant theoretic quotients for which semistability is not necessarily the…

We apply mapping class group techniques and trisections to study intersection forms of smooth 4-manifolds. Johnson defined a well-known homomorphism from the Torelli group of a compact surface. Morita later showed that every homology…

We prove that pseudoholomorphic curves intersect complex 2-cycles positively in almost complex 4-manifolds. This makes possible a general and conceptually simple proof that an almost complex 4-manifold with many curves admits a taming…

In this note we classify the diffeomorphism classes rel. boundary of smooth h-cobordisms between two fixed 1-connected 4-manifolds in terms of isometries between the intersection forms.

This paper provides a convenient and practical method to compute the homology and intersection pairing of a branched double cover of the 4-ball. To projections of links in the 3-ball, and to projections of surfaces in the 4-ball into the…

We establish a new homological lower bound for the Thurston norm on 1-cohomology of 3-manifolds. This generalizes previous results of C. McMullen, S. Harvey, and the author. We also establish an analogous lower bound for 1-cohomology of…

We will provide bounds on both the Betti numbers and the torsion part of the homology of hyperbolic orbifolds. These bounds are linear in the volume and are a direct consequence of an efficient simplicial model of the thick part, which we…

We show that the Thurston seminorms of all finite covers of an aspherical 3-manifold determine whether it is a graph manifold, a mixed 3-manifold or hyperbolic.

This is a note on calculating intersection numbers on moduli spaces of curves. A codimension 3 relation among tautological classes on the moduli space of genus 4 curves is given.

An important problem in quaternionic hyperbolic geometry is to classify ordered $m$-tuples of pairwise distinct points in the closure of quaternionic hyperbolic n-space, $\overline{{\bf H}_\bh^n}$, up to congruence in the holomorphic…

There are six orientable, compact, flat 3-manifolds that can occur as cusp cross-sections of hyperbolic 4-manifolds. This paper provides criteria for exactly when a given commensurability class of arithmetic hyperbolic 4-manifolds contains…

An interesting problem in solid state physics is to compute discrete breather solutions in $\mathcal{N}$ coupled 1--dimensional Hamiltonian particle chains and investigate the richness of their interactions. One way to do this is to compute…

We provide a novel proof of the homological excess intersection formula for local complete intersections. The novelty is that the proof makes use of global morphisms comparing the intersections to a self intersection.