Using the concept of s-formality we are able to extend the bounds of a Theorem of Miller and show that a compact k-connected 4k+3- or 4k+4-manifold with b_{k+1}=1 is formal. We study k connected n-manifolds, n= 4k+3, 4k+4, with a hard Lefschetz-like property and prove that in this case if b_{k+1}=2, then the manifold i…
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23 results for “k-connection”
Short note proves Lie algebroid deformation cohomology preservation under fibration conditions.
problem Understanding deformation cohomology of Lie algebroids under fibration conditions.
method Proves preservation of deformation cohomology up to degree k for Lie algebroids under certain fibration conditions.
result Deformation cohomology of Lie algebroids is preserved up to degree k under specified fibration conditions.
Reduces k-symplectic field theory equations and discusses reconstruction methods.
problem Reduction and reconstruction of k-symplectic field theory equations.
method Explicit coordinate expressions of reduced equations, interpretation of integrability conditions, introduction of k-connection.
result Invariant Lagrangian defines a mechanical k-connection for reconstruction.
We obtain estimations for isotopy classes of embeddings of closed k-connected n-manifolds into R^{2n-k-1} for n>2k+5 and k\ge0. This is done in terms of an exact sequence involving the Whitney invariants and an explicitly constructed action of H_{k+1}(N;Z_2) on the set of embeddings. (For k\ne1 classification results w…
Let be a differentiable manifold endowed with a transitive action of a Lie group . Let be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: {enumerate} equ…
We show that for every symmetric space G/K of compact type with K connected, the K-action on G/K by left translations is equivariantly formal.
Flat connections derived from Poisson brackets on loop spaces.
problem Understanding the structure of Poisson brackets on loop spaces.
method Defined connections by explicit linear combinations of standard connections associated with the Poisson bracket.
result Connections are shown to be flat.
The paper extends the formal manifold theorem to higher dimensions and characterizes -minimal models for certain differential graded algebras.
problem Characterizing formal differential graded algebras and their -minimal models.
method Expanding the formal manifold theorem and proving properties of -minimal models for specific cases.
result The de Rham complex of certain differential graded algebras has -minimal models with specific non-trivial terms.
An immersion of a compact manifold is tight if it admits the minimal total absolute curvature over all immersions of the manifold. A prominent result in the study of minimal total absolute curvature immersions is the theorem of Chern and Lashof, which characterizes minimal total absolute curvature immersions, and tight…
The paper proves eigenvalues are simple for specific operators on bundles.
problem Eigenvalue simplicity for connection Laplacian and -simplicity on bundles.
method Analyzes connections on vector bundles and principal bundles, proving eigenvalue simplicity for a residual set of connections.
result Eigenvalues of the connection Laplacian and Laplace-Beltrami operator are simple for specified conditions.
New groups connect braids and 3-manifolds.
problem Understanding relationships between braids and 3-manifolds.
method Introducing and studying groups .
result Groups lead to new relationships between braids and manifolds.
New findings on metric spaces with finite Nagata dimension.
problem Understanding isoperimetric properties in subsets of metric spaces.
method Analyzing quasiconvex subsets with finite Nagata dimension and applying isoperimetric inequalities.
result Quasiconvex subsets of metric spaces with finite Nagata dimension are isoperimetrically undistorted up to a certain dimension.
Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operatorsmath.DG
We examine questions of geometric realizability for algebraic structures which arise naturally in affine and Riemannian geometry. Suppose given an algebraic curvature operator R at a point P of a manifold M and suppose given a real analytic (resp. C-k for finite k at least 2) pseudo-Riemannian metric on M defined near …
We investigate quaternionic contact (qc) manifolds from the point of view of intrinsic torsion. We argue that the natural structure group for this geometry is a non-compact Lie group K containing Sp(n)H^*, and show that any qc structure gives rise to a canonical K-structure with constant intrinsic torsion, except in se…
The abstract discusses embedding manifolds in open books and contact structures.
problem Embedding manifolds in open books and contact structures.
method Using open book embeddings and contact structures, the abstract proves embedding theorems for various manifolds.
result Closed manifolds can be embedded in open books and contact structures.
The k-dimensional Dehn (or isoperimetric) function of a group bounds the volume of efficient ball-fillings of k-spheres mapped into k-connected spaces on which the group acts properly and cocompactly; the bound is given as a function of the volume of the sphere. We advance significantly the observed range of behavior f…
The paper finds solutions to the Yamabe equation with low energy and multiple nodal sets.
problem Finding solutions to the Yamabe equation with specific nodal structures.
method Reduction to a singular ODE and solving a double shooting problem.
result Existence of solutions with exactly k zeroes, yielding k connected isoparametric hypersurfaces as nodal sets.
This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find t…
The paper simplifies smooth maps to spheres and planes, showing homotopy and embedding properties.
problem Constructing explicit deformations of smooth maps to spheres and planes.
method Explicit constructions and homotopy arguments.
result Smooth maps are homotopic to stable maps with limited singularities.
The paper studies higher geometric structures and connections on manifolds, constructing moduli stacks and proving equivalence criteria.
problem Classifying and understanding higher geometric structures and connections on manifolds.
method Constructing smooth higher symmetry groups, moduli stacks, and higher gauge actions; proving equivalence criteria.
result Construction and classification of moduli stacks of higher geometric data and connections.
We show that an n-dimensional compactum X embeds in R^m, where m>3(n+1)/2, if and only if X x X - Δadmits an equivariant map to S^{m-1}. In particular, X embeds in R^{2n}, n>3, iff the top power of the (twisted) Euler class of the factor-exchanging involution on X x X - Δis trivial. Assuming that X quasi-embeds in R^{2…
This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K,C)-connections on a large class of 3-manifolds M with boundary. We define a space L_K(M) of framed flat connections on the boundary of M that extend to M. Our goal is to understand an open part of L_K(M)…
Study of groups and connects particle dynamics to manifold triangulations.
problem Understanding the relationship between particle dynamics and manifold triangulations.
method Introducing and studying groups and to connect dynamical systems to topological invariants.
result Found a topological invariant valued in for dynamical systems.