GRID invariants block certain Lagrangian cobordisms in 3D.
problem Obstructing decomposable Lagrangian cobordisms in 3D.
method Filtered GRID invariants and link Floer homology.
result GRID invariants obstruct decomposable Lagrangian cobordisms.
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48 results for “3D cobordism”
Study Seiberg-Witten moduli spaces on 3D cobordisms with Morse functions.
problem Properties of Seiberg-Witten moduli spaces on 3D cobordisms.
method Perturbed Seiberg-Witten equations on cylindrical ends with Morse functions.
result Properties of moduli spaces of Seiberg-Witten equations on 3D cobordisms.
New homology from 3D cobordism to integers.
problem Understanding 4-manifolds with boundary and their homology.
method Instanton homology with coefficients.
result Found a non-linear homomorphism with bounds on 4-manifolds.
Simplified 3D Dijkgraaf-Witten theory with defects explained geometrically.
problem Constructing 3D Dijkgraaf-Witten theory with defects.
method Symmetric monoidal functor from defect cobordism category to vector spaces, using geometric and homotopy theoretic methods.
result Explicit construction of 3D untwisted Dijkgraaf-Witten theory with defects.
Cyclic Objects from Surfacesmath.GT
The abstract introduces a new cyclic structure for surfaces.
problem Defining a cyclic structure for surfaces.
method Endowing surfaces with a structure of a (co)cyclic object in 3D cobordisms.
result 3D TQFTs induce (co)cyclic modules, which are computed algebraically.
Self-replicating 3-manifoldsmath.GT
The paper classifies self-replicating 3D shapes using algebraic models.
problem Understanding self-replicating 3D shapes.
method Using idempotents in the (2+1)-cobordism category to classify 3-manifolds.
result A classification theorem for self-replicating 3-manifolds.
Alternative algebraic characterization of 3D cobordisms category.
problem Characterize the category of 3D cobordisms algebraically.
method Define and prove equivalence of Hopf algebra categories and use a functor to present new axioms.
result Existence of a functor between Hopf algebra categories and implications for .
Homology handles with trivial Alexander polynomial bound a 3D sphere.
problem Understanding when homology handles bound 3D spheres.
method Using Freedman and Quinn's result for -homology 3-spheres.
result A distinguished homology handle with trivial Alexander polynomial bounds a homology .
Proves Giroux Correspondence in 3D using Heegaard splittings.
problem Proving Giroux Correspondence in 3D contact manifolds.
method Uses Heegaard splittings of contact manifolds, extending convex surface theory.
result Accessible proof for low-dimensional audience.
Solves asymptotic -realization problem for curves.
problem Realization problem for plane curves.
method Asymptotic analysis of smooth -realization.
result Determines cobordism distance between specific knot types.
New algebraic presentations for 3D cobordisms and 4D 2-handlebodies.
problem Finite algebraic presentations for cobordism and handlebody categories.
method Direct proof using a new functor construction.
result Algebraic presentations of 3Cob and 4HB categories.
Abstract TQFT for sutured manifolds using Floer homology.
problem Classical Frohman-Nicas TQFT for Alexander polynomial.
method Decategorification of bordered sutured Heegaard Floer homology.
result Generalization to arbitrary cobordisms between surfaces.
3D space without definite 4D counterpart found.
problem Finding 3-manifolds that don't bound definite 4-manifolds.
method Analysis of characteristic covectors in bimodular lattices.
result A rational homology 3-sphere that bounds no definite 4-manifold.
Study fermionic theories, their anomalies, and modular transformations.
problem Understanding fermionic theories and their anomalies.
method Use spin-cobordisms, surgeries, and invertible topological quantum field theories.
result Explicit combinatorial expressions for spin-bordism invariants.
We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independ…
The study extends cobordism theory to complex sections, defining and calculating cobordism groups.
problem Understanding when almost complex manifolds can have complex sections.
method Defined complex section cobordism, determined groups, and introduced an obstruction.
result The obstruction vanishes for certain multiplicative generators in the complex cobordism ring.
Study cobordisms of nested manifolds and their invariants.
problem Understanding cobordisms of nested manifolds and their invariants.
method Identify a nested analog of the Pontryagin-Thom construction and find spaces homotopy equivalent to nested Pontryagin-Thom spaces.
result Discover nested cobordism invariants and provide an alternative proof of Wall's splitting result.
The paper introduces a new invariant for cobordism classes of manifolds and extends cobordism groups.
problem Developing a new invariant for cobordism classes of manifolds.
method Introducing an invariant for null-cobordant -manifolds and constructing cobordism groups .
result The invariant is a complete invariant of -cobordism classes of null-cobordant -manifolds.
Defines cobordism maps connecting Khovanov and instanton homologies.
problem No direct correspondence between Khovanov and instanton homology cobordism maps.
method Defines a cobordism map on the instanton cube complex as a filtered chain map.
result Proves the cobordism map recovers both Khovanov and instanton homology cobordism maps.
The study explores conditions for -cobordisms between smooth 4-manifolds.
problem Determining when smoothly -cobordant 4-manifolds are also -cobordant.
method Providing new conditions for positive answers to the -cobordism theorem.
result Conditions under which standard methods to construct -cobordisms fail.
New formulas link string bordism to integers.
problem Understanding the third string bordism group.
method Geometric string structures and 3d TQFT.
result Integral formulas realize the string bordism isomorphism.
Study shows Khovanov homology's relation to decomposable Lagrangian cobordisms.
problem Understanding the relationship between Khovanov homology and decomposable Lagrangian cobordisms.
method Utilized previously defined filtered invariants to give obstructions.
result Partial answer to Ekholm, Honda, and Kálmán's question about Khovanov homology and decomposable Lagrangian cobordisms.
The article examines how many stabilizations are needed to transform 5D s-cobordisms into product cobordisms.
problem Understanding the number of stabilizations required to convert 5D s-cobordisms into product cobordisms.
method Utilizes Gabai's 4D light bulb theorem and Freedman Quinn invariant.
result Determines the number of stabilizations needed for 5D s-cobordisms.
Extends cobordism groups of immersions to projections with new results.
problem Understanding cobordism groups of projected immersions.
method Classifying space construction by Szűcs and Terpai, Salomonsen's exact sequence.
result Obtains results on cobordism groups in small and large codimensional cases.
We give complete geometric invariants of cobordisms of fold maps with oriented singular set and cobordisms of even codimensional fold maps. These invariants are given in terms of cobordisms of stably framed manifolds and cobordisms of immersions with prescribed normal bundles defined by the author in his earlier works.
Study exact Lagrangian cobordisms in cotangent bundles, proving bounds on sheaf interleaving distance and shadow distance.
problem Understanding Lagrangian cobordisms and their properties in cotangent bundles.
method Use microlocal theory of sheaves, sheaf quantization, and cone decompositions.
result Interleaving distance of sheaves is bounded by the shadow distance of the cobordism.
New results on algebraic knots with Brieskorn polynomials.
problem Understanding cobordisms of algebraic knots defined by Brieskorn polynomials.
method Analyzing Fox--Milnor type relations, decomposing algebraic cobordism classes, and studying cyclic suspensions.
result Spherical algebraic knots associated with Brieskorn polynomials have infinite order in the knot cobordism group.
On -cobordisms of complexity math.GT
Study -cobordisms of complexity 2 in 5D, finding obstructions and examples.
problem Understanding -cobordisms of complexity 2 in 5D.
method Compute monopole Floer homology and action of twisting involution.
result Obtained obstructions and constructed examples of high complexity.
Study finds conditions for existence of specific pseudo-Riemannian cobordisms.
problem Existence of Spin-dimensional cobordisms with specific signature.
method Analyzes Spin-dimensional cobordisms with signature .
result Computes cobordism groups and necessary/sufficient conditions for existence.
We study the problem of defining maps on link Floer homology induced by unoriented link cobordisms. We provide a natural notion of link cobordism, disoriented link cobordism, which tracks the motion of index zero and index three critical points. Then we construct a map on unoriented link Floer homology associated to a …
Topology change and selection rules for high-dimensional $\Spin(1, n)_0$-Lorentzian cobordismsmath.GT
We study necessary and sufficient conditions for the existence of Lorentzian and weak Lorentzian cobordisms between closed smooth manifolds of arbitrary dimension such that the structure group of the frame bundle of the cobordism is $\Spin(1, n)_0$. This extends a result of Gibbons-Hawking on $\Sl(2, \C)$-Lorentzian co…
Using methods inspired from algebraic -theory, we give a new proof of the Genauer fibration sequence, relating the cobordism categories of closed manifolds with cobordism categories of manifolds with boundaries, and of the Bökstedt-Madsen delooping of the cobordism category. Unlike the existing proofs, this approach…
We show that the theory of stable complex -cobordisms, for a torus , is embedded into the theory of stable complex -cobordisms of not necessarily compact manifolds equipped with proper abstract moment maps. Thus the introduction of such non-compact cobordisms in the stable complex -cobordism theory does not…
Cobordism of disk knotsmath.GT
We study cobordisms and cobordisms rel boundary of PL locally-flat disk knots $D^{n-2}\into D^n$. Cobordisms of disk knots that do not fix the boundary sphere knots are easily classified by the cobordism properties of these boundaries, and any two even-dimensional disk knots with isotopic boundary knots are cobordant r…
Researchers develop methods to construct Lagrangian cobordisms between Legendrian knots.
problem Understanding the relationship between Legendrian knots through Lagrangian cobordisms.
method Combinatorial and geometric methods, including Heegaard Floer Homology and contact surgery.
result Construction of nondecomposable Lagrangian cobordisms between Legendrian knots.
Periodic Floer homology (PFH) is a Gromov-Floer type invariant for fibered three-manifolds with Hamiltonian structures. The cobordism maps on periodic Floer homology induced by symplectic cobordisms are currently only defined indirectly by using Seiberg-Witten theory. In this paper, we investigate the cobordism maps in…
Paper extends cobordism maps in Khovanov and instanton homologies.
problem Define and prove compatibility of cobordism maps in Khovanov and instanton homologies.
method Extend embedded cobordism map to immersed cobordisms and prove compatibility.
result Induced map on Khovanov homology is injective for certain concordances.
We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.
New cobordisms found between certain quasipositive knots.
problem Existence of complex cobordisms between quasipositive knots.
method Construction of specific knots and cobordisms of specified genus.
result No complex cobordism exists between certain quasipositive knots.
Paper presents new cobordism sequences for singular maps.
problem Understanding cobordism groups of singular maps.
method Develops analogous exact sequences to classical ones.
result Positive answer to Szűcs' question on cobordisms of immersions.
The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nas…
Cobordism of wordsmath.CO
We introduce an equivalence relation, called cobordism, for words and study cobordism invariants of words inspired by methods of low-dimensional topology.
3-manifolds with specific homology are cobordant if homeomorphic.
problem Characterizing integer homology cobordism for Sol manifolds.
method Analyzing first homology groups and using cobordism theory.
result Integer homology cobordant Sol manifolds are homeomorphic.
Foam cobordism groups linked to interval exchange automorphisms.
problem Understanding cobordism groups of foams.
method Using the Sah-Arnoux-Fathi invariant and K-theory.
result Identified cobordism groups with homology and K-groups.
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 affirmative answer by introducing a natural notion of cobordism between sutured manifolds, and showing that such a cobordism induces a map on sutured F…
Study on knot concordance and homology cobordism using Heegaard Floer homology.
problem Knot concordance and homology cobordism.
method Heegaard Floer homology.
result Recent results in knot concordance and homology cobordism.
Study shows mapping class groups differ for -cobordant manifolds.
problem Mapping class groups are invariant under -cobordism.
method Introduced moduli spaces of -block bundles to distinguish manifolds.
result Mapping class groups of -cobordant manifolds can differ.
In this article, we reformulate the cobordism map of embedded contact homology, which is induced by exact symplectic cobordism and defined as direct limit of homomorphisms called filtered ECH cobordism map. The filtered ECH cobordism map is defined by counting embedded holomorphic curves with zero ECH index and we prov…