New exotic 4-manifolds found with fiber bundles.
problem Finding non-diffeomorphic exotic 4-manifolds.
method Smooth fiber bundles over the circle.
result Exotic 4-manifolds with non-simply-connected fiber.
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48 results for “topological 4-manifold bundles”
Every 1-connected topological 4-manifold M admits a -covering by $#_{r-1}S^{2}\times S^{3}$, where rank$H^{2}(M;\QTR{Bbb}{Z})$.
New configuration space integrals show nontrivial formal smooth structures on 4-manifold bundles.
problem Disproving the 4-dimensional Smale conjecture by constructing nontrivial bundles.
method Defining new configuration space integrals relying on formal smooth structures.
result Discovering a generalized Miller-Morita-Mumford class obstructing formal smooth structures.
Involutory Hopf group-coalgebras provide new invariants for 4-manifold bundles.
problem Developing invariants for flat bundles over 4-manifolds.
method Utilizing Hopf -triplets and colored trisection diagrams.
result Involutory Hopf -triplets yield well-defined invariants of -colored trisection diagrams.
We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0,1) supersymmetry and, possibly, a residual flavor symmetry. …
Algorithm trisects 4D book into three chapters.
problem Trisecting 4D book into chapters.
method Algorithm for open book decompositions of 4-manifolds.
result Algorithm works for various types of manifolds.
Study shows only two topological configurations for Spin(7)-manifold fibrations, ruling out smooth Cayley fibrations.
problem Understanding smooth fibrations of compact Spin(7)-manifolds by Cayley submanifolds.
method Geometric and topological constraints from Spin(7)-structure, spinnability criterion, gauge-theoretic input.
result Rules out smooth Cayley fibrations on all known compact torsion-free Spin(7)-manifolds.
Classification of homogeneous almost complex 4-manifolds with non-degenerate torsion bundle
problem Classification of homogeneous almost complex 4-manifolds with non-degenerate torsion bundle
method Classification using rigidity of structures
result Complete classification in the homogeneous setting
Let M be a 4-manifold with residually finite fundamental group G having b_1(G) > 0. Assume that M carries a symplectic structure with trivial canonical class K = 0 in H^2(M). Using a theorem of Bauer and Li, together with some classical results in 4-manifold topology, we show that for a large class of groups $ is deter…
Sphere bundles over 4-manifolds are trivial after looping, except for two cases.
problem Understanding the triviality of sphere bundles over 4-manifolds.
method Analyzing the splitting of sphere bundles after looping.
result The loop spaces of total manifolds of sphere bundles are homotopy equivalent, except for two special cases.
The study bounds the excess of disjoint nonorientable surfaces in a 4-manifold.
problem Bounding the excess of disjoint nonorientable surfaces in a 4-manifold.
method Combining tubing construction with signature and Euler-characteristic formulas for 2-fold branched covers.
result The normal-Euler excess is bounded by a constant depending only on the ambient 4-manifold.
In this paper, we prove the existence of certain symplectic conifold transitions on all -bundles over symplectic 4--manifolds, which generalizes Smith, Thomas and Yau's examples of symplectic conifold transitions on trivial -bundles over Kähler surfaces. Our main result is to determine the diffeomorphis…
The paper classifies and studies symplectic and contact properties of circular spherical divisors.
problem Investigating symplectic and contact topology of circular spherical divisors.
method Classification and analysis of concave circular spherical divisors, including embedding, Stein fillability, and rational homology type determination.
result All concave circular spherical divisors up to toric equivalence are realized as symplectic log Calabi-Yau pairs with minimal complements.
We prove an existence theorem for gauge invariant -normal neighborhoods of the reduction loci in the space of oriented connections on a fixed Hermitian 2-bundle . We use this to obtain results on the topology of the moduli space of (non-necessarily irreducible) oriented connectio…
Yang-Mills energy quantization over non-collapsed degenerating Einstein manifolds and applicationsmath.DG
Study quantizes topological numbers on degenerating Einstein manifolds.
problem Quantizing topological numbers on non-collapsed degenerating Einstein manifolds.
method Compactness theory of bubbles, classical vanishing theorems, and Hirzebruch-Riemann-Roch theorems.
result Established quantization results for various topological numbers.
Conditions for equivariant bundles on 4-manifolds with cyclic actions.
problem Existence of equivariant bundles on 4-manifolds with cyclic actions.
method Conditions derived from the twisted signature formula and congruence relations between fixed point data and isotropy representations.
result Necessary and sufficient conditions for the existence of equivariant bundles.
Computes mapping class groups of 4-manifolds with boundary.
problem Computing mapping class groups for 4-manifolds with boundary.
method Topological and smooth methods applied to compact, simply connected 4-manifolds.
result Description of topological and stable smooth mapping class groups.
In this paper we obtain the following results: (1) Any compact Stein surface with boundary embeds naturally into a symplectic Lefschetz fibration over the 2-sphere. (2) There exists a minimal elliptic fibration over the 2-disk, which is not Stein. (3) The circle bundle over a genus n>1 surface with euler number e=-1 ad…
New smoothing techniques for topological surfaces in 4-manifolds.
problem Topological isotopy of surfaces in smooth 4-manifolds.
method Combining Quinn's smoothing theory with Gabai's light bulb theorem and other developments.
result Proves topological = smooth results for certain disks and spheres.
We present an approach to constructing broken Lefschetz fibrations (BLFs) from a handle decomposition of a 4-manifold . Given a handle decomposition as input these techniques yield explicit descriptions of the BLFs, and do not rely on classification results from contact topology or the choice of…
Study finite group actions on symplectic Calabi-Yau 4-manifolds with non-zero first Betti number.
problem Determine fixed-point set structure of symplectic Calabi-Yau 4-manifolds with certain group actions.
method Analysis of symplectic surfaces and disjoint embeddings in rational 4-manifolds.
result Symplectic Calabi-Yau 4-manifolds are shown to be -bundles under specific group actions.
New invariant for classifying 4-manifolds up to cobordism.
problem Classifying closed, oriented topological 4-manifolds up to -cobordism.
method Introducing a stable range invariant after stabilization by a fixed number of .
result A new invariant for classifying 4-manifolds up to -cobordism.
The abstract explains counterexamples in 4-manifold topology.
problem Understanding the equivalence relations on 4-manifolds.
method Explains and provides counterexamples for various equivalence relations.
result Illustrates the failure of potential implications between equivalence relations.
Classifies torus bundles bounding 4-manifolds with rational homology.
problem Classifying torus bundles over the circle that bound 4-manifolds with rational homology.
method Completely classified torus bundles over the circle that bound 4-manifolds with rational homology.
result Completely classified torus bundles over the circle that bound 4-manifolds with rational homology.
Manufacturing infinite sets of knotted and unknotted surfaces in 4-manifolds.
problem Creating infinite sets of knotted and unknotted surfaces in 4-manifolds.
method Recent constructions of inequivalent smooth structures.
result Infinite sets of pairwise smoothly non-isotopic nullhomologous 2-tori and spheres.
Study evaluates topological contributions in massive SQCD on compact 4-manifolds.
problem Analyzing topological path integrals for massive SQCD with up to 3 massive hypermultiplets.
method Decouples hypermultiplets, evaluates massless limit, and merges singularities at Argyres-Douglas points. Uses mass expansions for and .
result Physical partition functions match mathematical results on Segre numbers of instanton moduli spaces.
New method to decompose 4-manifolds with positive scalar curvature.
problem Understanding and decomposing 4-manifolds with positive scalar curvature.
method 0 and 1-surgeries on topologically PSC 4-orbifolds.
result Every closed, oriented, topologically PSC 4-manifold can be obtained from a specific type of 4-orbifold.
New stable minimal hypersurfaces found in 4-manifolds, proving topology results.
problem Finding stable minimal hypersurfaces with specific topologies in 4-manifolds.
method Geometric measure theory and 4-manifold topology techniques.
result Existence of stable minimal hypersurfaces diffeomorphic to or .
We construct examples of non-isotrivial algebraic families of smooth complex projective curves over a curve of genus 2. This solves a problem from Kirby's list of problems in low-dimensional topology. Namely, we show that 2 is the smallest possible base genus that can occur in a 4-manifold of non-zero signature which i…
Algorithm decides homeomorphism of 4-manifolds.
problem Deciding homeomorphism of closed, simply connected 4-manifolds.
method Represent 4-manifolds by Kirby diagrams, compute Kirby-Siebenmann invariant, and use algorithms for Kirby diagrams and intersection forms.
result Algorithmic decision for homeomorphism of 4-manifolds.
We prove that compact topological 4-manifolds can be effectively presented by a finite amount of data.
We show a rigidity theorem for the Seiberg-Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type inequality. As an application, we prove the existence of non-smoothable topological families of 4-manifolds whose fiber, base space, and tota…
New examples of knotting phenomena in 4-manifolds with specific fundamental groups.
problem Finding 2-spheres in simply connected 4-manifolds with prescribed fundamental groups.
method Construction of infinite sets of pairwise smoothly inequivalent 2-spheres that are topologically isotopic.
result First known examples of knotting phenomena in 4-manifolds with specific properties.
In this paper we exhibit infinite families of embedded tori in 4-manifolds that are topologically isotopic but smoothly distinct. The interesting thing about these tori is that they are topologically trivial in the sense that each bounds a topologically embedded solid handlebody. This implies that there are stably ribb…
This paper considers aspects of 4-manifold topology from the point of view of the null cone of a neutral metric, a point of view we call neutral causal topology. In particular, we construct and investigate neutral 4-manifolds with null boundaries that arise from canonical 3- and 4-dimensional settings. A null hypersurf…
Link homology theories connect to 4-manifold invariants and TQFTs.
problem Connecting link homology theories to 4-manifold invariants and TQFTs.
method Functorial link homologies, skein modules, handle decompositions.
result Link homology theories become diagram-independent and furnish invariants of 4-manifolds.
Study on topological pseudo-isotopies of 4-manifolds, proving some cases and finding counterexamples.
problem Determining when a topologically pseudo-isotopic diffeomorphism is also smoothly pseudo-isotopic.
method Analyzing the fundamental group of 4-manifolds and constructing counterexamples.
result Some fundamental groups guarantee a positive answer, while others can have negative outcomes.
Improved proofs for topological and smooth pseudo-isotopies of simply connected 4-manifolds.
problem Proving topological and smooth pseudo-isotopies of simply connected 4-manifolds.
method Provided different arguments that bypass the replacement criterion, thus completing Quinn's proofs.
result Corrected and completed Quinn's proofs of both topological and stable smooth pseudo-isotopy theorems.
New definition of skein lasagna module for specific 4-manifolds.
problem Defining a new homology theory for specific 4-manifolds.
method Elementary definition using diagrams in the 4-manifold.
result Explicit calculations for disk bundles over S^2.
Study finds topological restrictions on 4-manifolds with uniformly positive scalar curvature.
problem Understanding which 4-manifolds can have metrics with uniformly positive scalar curvature.
method Topological obstructions and metric constructions on specific 4-manifolds.
result Existence of uncountably many exotic 's without such metrics and topological uniqueness of certain metrics.
Symplectic 4-manifolds with Kodaira dimension zero can be viewed as symplectic Calabi-Yau surfaces. We are able to completely determine their Betti numbers by proving two general results on quaternionic vector bundles.
This is a slightly altered version of the authors thesis from 2014. In the first main part we show that the quotient space of a compact, simply connected and nonnegatively curved Riemannian 4-manifold by an effective, isometric circle-action admits an approximation in Gromov-Hausdorff topology by smooth, positively cur…
The paper constructs symplectic forms on 4-manifolds using branched coverings and holomorphic line bundles.
problem Constructing symplectic forms on 4-manifolds with rational symplectic forms.
method Using branched coverings and holomorphic line bundles, the paper constructs symplectic forms that are Kähler in a neighborhood of the 2-skeleton of the manifold.
result The paper proves the existence of a cohomologous symplectic form that is Kähler in a neighborhood of the 2-skeleton of the manifold.
We show that infinitely many of the simply connected 4-manifolds constructed by Levine and Lidman that do not admit PL spines actually admit topological spines.
Study surfaces in 4-manifolds with cyclic fundamental group.
problem Characterize surfaces with infinite cyclic knot group.
method Algebraic topological criteria and homeomorphism proofs.
result Ambiently isotopic surfaces with the same genus have a homeomorphism.
This paper constructs a Weinstein trisection for a surface bundle.
problem Constructing a trisection for a surface bundle.
method Weinstein trisection approach applied to .
result Explicit construction of a Weinstein trisection for .
New classification of nonorientable 4-manifolds with specific fundamental groups.
problem Classifying nonorientable 4-manifolds with cyclic fundamental groups.
method Simple cut-and-paste construction, using results from Hambleton-Kreck-Teichner and Khan.
result Plausible classification of a large set of nonorientable 4-manifolds with cyclic fundamental groups of order 2p.
4-manifolds with non-positive curvature are essentially Euclidean.
problem Understanding the structure of 4-manifolds with specific curvature properties.
method Proving homeomorphism to Euclidean space using globally non-positive curvature.
result CAT(0) 4-manifolds are homeomorphic to Euclidean space.