arXiv research

This paper formalizes manifolds in positive characteristic varieties.

New group-theoretic Johnson classes applied to curves with torsion Ceresa classes.

Establishes Poincaré's lemma for formal manifolds.

Foundations laid for formal manifolds in differential geometry.

Explores local structure of morphisms and formal submanifolds in formal manifolds theory.

Strong formal properties for toric and homogeneous Kähler manifolds.

Formal manifolds with non-negative Ricci curvature have formal covers.

The study shows strong formality in certain complex manifolds.

Defines formal exponentials for graded manifolds and linearizes QP-manifolds.

Study on geometrically formal metrics on complex manifolds.

Research on formality problem for special holonomy manifolds.

Extended equivariant BV formalism to manifolds with boundaries.

Paper applies Newman-Penrose formalism to ACM manifolds.

Non-formal G2 manifold found with holonomy.

We discuss the question of geometric formality for rationally elliptic manifolds of dimension $6$ and $7$. We prove that a geometrically formal six-dimensional biquotient with $b_{2}=3$ has the real cohomology of a symmetric space. We also show that a rationally hyperbolic six-dimensional manifold with $b_2\leq 2$ and …

New findings on complex manifold properties under deformations.

New examples of non-formal Sasaki-Einstein 7-manifolds and their submanifolds found.

A Riemannian manifold is called geometrically formal if the wedge product of harmonic forms is again harmonic, which implies in the compact case that the manifold is topologically formal in the sense of rational homotopy theory. A manifold admitting a Riemannian metric of positive sectional curvature is conjectured to …

The paper proves a quadratic formality for Sasakian manifolds' representation varieties.

In this paper, we study the formal solution space of a nonlinear PDE in a fiber bundle. To this end, we start with foundational material and introduce the notion of a pfd structure to build up a new concept of profinite dimensional manifolds. We show that the infinite jet space of the fiber bundle is a profinite dimens…

Compact non-formal $G_2$ manifold with $b_1=1$.

We prove that any simply connected compact 3-Sasakian manifold, of dimension seven, is formal if and only if its second Betti number is $b_2<2$. In the opposite, we show an example of a 7-dimensional Sasaki-Einstein manifold, with second Betti number $b_2\geq 2$, which is formal. Therefore, such an example does not adm…

Introduces formal frames for manifolds and their properties.

The abstract manifold cannot have uniformly quasiregular self-maps.

The article confirms Joyce's examples of G2-holonomy are formal spaces.

A Riemannian manifold is called geometrically formal if the wedge product of any two harmonic forms is again harmonic. We classify geometrically formal compact 4-manifolds with nonnegative sectional curvature. If the sectional curvature is strictly positive, the manifold must be homeomorphic to S^4 or diffeomorphic to …

This paper shows hypercommutative algebras on Calabi-Yau manifolds are formal.

Abstract study of HKT manifolds, proving Hodge theory and formality properties.

We construct examples of non-formal simply connected and compact oriented manifolds of any dimension bigger or equal to 7.

A knot space in a manifold M is a space of oriented immersions from a circle S^1 to M up to Diff(S^1). Brylinski has shown that a knot space of a Riemannian threefold is formally Kahler. We prove that a space of knots in a holonomy G2 manifold is formally Kahler.

We investigate some topological properties, in particular formality, of compact Sasakian manifolds. Answering some questions raised by Boyer and Galicki, we prove that all higher (than three) Massey products on any compact Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian structures. Using th…

Study bigraded formality and Aeppli-Bott-Chern-Massey products on complex manifolds.

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…

The paper proves conditions for 2-torus manifolds to be equivariantly formal.

A conjecture of Hirschowitz's predicts that a globally generated vector bundle $W$ on a compact complex manifold $A$ satisfies the formal principle, i.e., the formal neighborhood of its zero section determines the germ of neighborhoods in the underlying complex manifold of the vector bundle $W$. By applying Cartan's eq…

Quantizes functions on Kähler manifolds without formal deformation.

The paper examines metrics on foliated manifolds that have special geometric properties.

We prove the formality and the evenness of odd-degree Betti numbers for compact Kähler orbifolds, by adapting the classical proofs for Kähler manifolds. As a consequence, we obtain examples of symplectic orbifolds not admitting any Kähler orbifold structure. We also review the known examples of non-formal simply connec…

We investigate harmonic forms of geometrically formal metrics, which are defined as those having the exterior product of any two harmonic forms still harmonic. We prove that a formal Sasakian metric can exist only on a real cohomology sphere and that holomorphic forms of a formal Kähler metric are parallel w.r.t. the L…

A metric is formal if all products of harmonic forms are again harmonic. The existence of a formal metric implies Sullivan formality of the manifold, and hence formal metrics can exist only in presence of a very restricted topology. We show that a warped product metric is formal if and only if the warping function is c…

For a closed Kähler manifold with a Hamiltonian action of a connected compact Lie group by holomorphic isometries, we construct a formal Frobenius manifold structure on the equivariant cohomology by exploiting a natural DGBV algebra structure on the Cartan model.

Generalizes Tulczyjew triples for contact manifolds in Hamiltonian and Lagrangian formalisms.

Holomorphic bundles on complex manifolds with boundary are studied, extending results from Donaldson's work.

We study a geometric notion related to formality for Bott-Chern cohomology on complex manifolds.

Inspired by a work of Kapranov, we define the notion of Dolbeault complex of the formal neighborhood of a closed embedding of complex manifolds. This construction allows us to study coherent sheaves over the formal neighborhood via complex analytic approach, as in the case of usual complex manifolds and their Dolbeault…

Let (M, π ) be a Poisson manifold. A Poisson submanifold $P \in M$ gives rise to an algebroid $AP \rightarrow P$, to which we associate certain chomology groups which control formal deformations of π around P . Assuming that these groups vanish, we prove that π is formally rigid around P , i.e. any other Poisson struct…

We study the formality of the mapping torus of an orientation-preserving diffeomorphism of a manifold. In particular, we give conditions under which a mapping torus has a non-zero Massey product. As an application we prove that there are non-formal compact co-symplectic manifolds of dimension $m$ and with first Betti n…

Formal Normal Form created for special CR singularities.