arXiv research

Let X be a smooth closed oriented non-spin 4-manifold with even intersection form kE_8\oplus nH. In this article we show that n\geq |k| on X. Thus we confirm the 10/8-conjecture affirmatively. As an application, we also give an estimate of intersection forms of spin coverings of non-spin 4-manifolds with even intersect…

Researchers construct irreducible 4-manifolds with specific properties.

We extend a result of M. Katz on conformal systoles to all four-manifolds with b^+=1 which have odd intersection form. The same result holds for all four-manifolds with b^+=1 with even intersection form and which are symplectic or satisfy the so-called 5/4-conjecture.

Proves intersection properties of minimal hypersurfaces in various spaces.

In this paper, we exploit a subtle indeterminacy in the definition of the spherical Kervaire-Milnor invariant which was discovered by R. Stong to construct non-spin 4-manifolds with even intersection form and prescribed signature.

In this paper, we prove a number of inequalities between the signature and the Betti numbers of a 4-manifold with even intersection form. Furthermore, we introduce a new geometric group invariant and discuss some of its properties.

New exotic structures found on 4-manifolds with specific groups.

Study refines Siegel-Veech constants for abelian differentials.

We prove an extension of the Cheeger-Müller theorem to spaces with isolated conical singularities: the $L^2$-analytic torsion coincides with the Ray-Singer intersection torsion on an even dimensional space, and they are trivial, while the ratio is non trivial on an odd dimensional space, and the anomaly depends only on…

Wall's result extended to 4-manifolds with definite intersection forms.

New metric found for 4-manifolds with specific properties.

In this paper we construct families of homology spheres which bound 4-manifolds with intersection forms isomorphic to $-E_8$. We show that these families have arbitrary large correction terms. This result says that among homology spheres, the difference of the maximal rank of minimal sub-lattice of definite filling and…

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

Minimum algebraic intersection found in hyperbolic surfaces, growing with genus.

New method to compute homology and intersection form of 4-manifolds.

The study finds non-contractible geodesics on compact Finsler space forms without intersections.

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 $H_1(Σ;\mathbb{Z})$ generated by the three sets of curves and the intersection pairing on the diagram surface $Σ$. This includes explicit formulas for the second and third h…

We prove a quantitative statement of the quantum ergodicity for Hecke--Maass cusp forms on the modular surface. As an application of our result, along a density $1$ subsequence of even Hecke--Maass cusp forms, we obtain a sharp lower bound for the $L^2$-norm of the restriction to a fixed compact geodesic segment of $η=…

New lower bounds show learning intersections of halfspaces is hard even for a few halfspaces.

We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds.

Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume $\frac{34π^2}{3}\cdot 16$ by using the small cover theory. In particular, we classif…

The first part of this paper exposits a simple geometric description of the Kirby-Siebenmann invariant of a 4--manifold in terms of a quadratic refinement of its intersection form. This is the first in a sequence of higher-order intersection invariants of Whitney towers studied by the authors, particularly for the 4--b…

A proof via the Seiberg-Witten moduli space of Donaldson's theorem on smooth 4-manifolds with definite intersection forms.

Using Seiberg-Witten Floer spectrum and Pin(2)-equivariant KO-theory, we prove new Furuta-type inequalities on the intersection forms of spin cobordisms between homology $3$-spheres. As an application, we give explicit constrains on the intersection forms of spin $4$-manifolds bounded by Brieskorn spheres $\pmΣ(2,3,6k\…

Let $X$ be any subanalytic compact pseudomanifold. We show a De Rham theorem for $L^\infty$ forms. We prove that the cohomology of $L^\infty$ forms is isomorphic to intersection cohomology in the maximal perversity.

Algorithm corrects bias in classification data.

We address the problem of computing bounds for the self-intersection number (the minimum number of self-intersection points) of members of a free homotopy class of curves in the doubly-punctured plane as a function of their combinatorial length L; this is the number of letters required for a minimal description of the …

Paper calculates homology and intersection form of trisected 4-manifolds with boundary.

Study the intersection form on Kähler manifolds of dimension 4 and above.

The study sets constraints on 4-manifold forms linked to specific invariants.

The paper explores existence of specific almost complex manifolds with unique Betti numbers.

Given a closed, oriented surface M, the algebraic intersection of closed curves induces a symplectic form Int(.,.) on the first homology group of M. If M is equipped with a Riemannian metric g, the first homology group of M inherits a norm, called the stable norm. We study the norm of the bilinear form Int(.,.), with r…

We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg and Murphy [6], that every odd-dimensional moment-angle manifold admits a contact …

Torsion sensitive intersection homology was introduced to unify several versions of Poincare duality for stratified spaces into a single theorem. This unified duality theorem holds with ground coefficients in an arbitrary PID and with no local cohomology conditions on the underlying space. In this paper we consider for…

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 3-sphere can be obtained from the standard Heegaard decomposition of $S^3$ by regluing…

A new method improves AI fairness assessment by estimating performance across intersectional subgroups.

This paper presents a novel framework for accurate pedestrian intent prediction at intersections. Given some prior knowledge of the curbside geometry, the presented framework can accurately predict pedestrian trajectories, even in new intersections that it has not been trained on. This is achieved by making use of the …

This note proves combinatorially that the intersection pairing on the middle dimensional compactly supported cohomology of a smooth toric hyperkaehler variety is always definite, providing a large number of non-trivial L^2 harmonic forms for toric hyperkaehler metrics on these varieties. This is motivated by a result o…

Extended surgery theory proves diffeomorphism for simply-connected 4k-manifolds.

We study the properties of geodesic currents on free groups, particularly the "intersection form" that is similar to Bonahon's notion of the intersection number between geodesic currents on hyperbolic surfaces.

To each ribbon graph we assign a so-called L-space, which is a Lagrangian subspace in an even-dimensional vector space with the standard symplectic form. This invariant generalizes the notion of the intersection matrix of a chord diagram. Moreover, the actions of Morse perestroikas (or taking a partial dual) and Vassil…

Proves Frankel theorem for generic submanifolds in Sasakian manifolds.

Four counterexamples in surface homology.

Gay and Kirby introduced trisections which describe any closed oriented smooth 4-manifold $X$ as a union of three four-dimensional handlebodies. A trisection is encoded in a diagram, namely three collections of curves in a closed oriented surface $Σ$, guiding the gluing of the handlebodies. Any morphism $\varphi$ from …

We determine the contributions of isolated singularities of spin V 4-manifolds to the index of the Dirac operator over them. From these data we derive certain constraints on the intersection forms of spin 4-manifolds bounded by spherical 3-manifolds, and also on the embeddings of the real projective planes into 4-manif…

We calculate eigenvector overlaps between intersecting time periods of covariance matrices.

Formula for computing triple-cup product from Heegaard diagrams of 3-manifolds.

Moduli spaces of hyperbolic surfaces with geodesic boundary components of fixed lengths may be endowed with a symplectic structure via the Weil-Petersson form. We show that, as the boundary lengths are sent to infinity, the Weil-Petersson form converges to a piecewise linear form first defined by Kontsevich. The proof …