arXiv research

New cohomological obstruction found for astheno-Kahler metrics.

Obstructing deformations of vector forms on Kähler manifolds.

Paper finds a cohomological obstruction to compact Clifford-Klein forms existence.

Obstructions found for closed Fedosov star products on symplectic and Kähler manifolds.

Unified understanding of integrability obstructions for Lie algebroids.

Obstruction found for embedding 3-spheres into a specific 4-manifold.

We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological obstructions for the existence of b-log symplectic structures similar to those in symplectic geometry.

Analyzes complex structure deformations using cohomology contraction methods.

Develops obstruction theory for a specific 4-manifold index.

Study on symplectic structures and their deformations.

Study classifies symmetric spaces without compact models.

The paper studies spectral sequences on Vaisman manifolds and finds cohomological obstructions.

Braid groups relate to disk diffeomorphisms with punctures.

Integrable Pfaffian systems invariant under Lie group actions have their cohomology equal to Lie algebra cohomology.

Study shows cohomological limits on extending actions on 3-manifold boundaries.

The study classifies nilpotent Lie foliations with cohomological obstructions.

A space is created to realize a specific cohomology module, showing PL structure but not smoothability.

The paper develops obstructions for embedding 2D complexes into 4D space.

The technique of generating families produces obstructions to the existence of embedded Lagrangian cobordisms between Legendrian submanifolds in the symplectizations of 1-jet bundles. In fact, generating families may be used to construct a TQFT-like theory that, in addition to giving the aforementioned obstructions, yi…

Squeezed knots are slices of minimal cobordisms; obstructions come from quantum knot invariants.

Study on deformation theory of nearly G2 manifolds with obstructions.

Study cohomological equation for robotic screw motions on SE(3).

Study on geometrically formal metrics on complex manifolds.

Decouples moduli groups in heterotic string theory cohomology.

Odaka and Wang proved the intersection formula for the Donaldson-Futaki invariant. In this paper, we generalize this result for the higher Futaki invariants which are obstructions to asymptotic Chow semistability.

Study on deformation cohomology for braided commutative structures.

We propose a produre of reduction a locally conformal symplectic structure. This procedure of reduction can be applied to wide class of submanifolds. There are no local obstructions for this procedure. But there are global obstructions. We find a necessary and sufficient condition when this reduction holds in terms of …

This paper develops a cohomological hierarchy for bistable visual paradoxes.

Let $X$ be a compact complex manifold, consider a small deformation $φ: \mathcal{X} \to B$ of $X$, the dimensions of the cohomology groups of tangent sheaf $H^q(X_t,\mathcal{T}_{X_t})$ may vary under this deformation. This paper will study such phenomenons by studying the obstructions to deform a class in $H^q(X,\mathc…

Non-trivial obstructions found for topological solitons in Yang-Mills-Chern-Simons theories.

We compute the Chen-Ruan orbifold cohomology ring of the Batyrev mirror orbifold of a smooth quintic hypersurface in 4-dimensional projective space. We identify the obstruction bundle for this example by using the Riemann bilinear relations for periods. We outline a general method of computing the Chen-Ruan ring for Ca…

Develops equivariant Seiberg-Witten-Floer cohomology for 3-spheres.

Let $M$ be a compact abstract $CR$ manifold of arbitrary $CR$ codimension. Under certain conditions on the Levi form we prove the infinite dimensionality of some global cohomology groups of $M$.

The article provides obstructions for exact submanifolds in symplectic applications.

Study on Čech-de Rham obstruction in diffeological spaces.

Two examples of $\mathrm{Diff}^+S^1$-invariant closed two-forms obtained from forms on jet bundles, which does not admit equivariant moment maps are presented. The corresponding cohomological obstruction is computed and shown to coincide with a nontrivial Lie algebra cohomology class on $H^2(\mathfrak{X}(S^1))$.

Classifies stable diffeomorphism of spin 4-manifolds with specific fundamental groups.

Proves section conjecture for curves and surface bundles over various fields.

Solves Kobayashi's conjecture on homogeneous spaces.

Characterizes obstacles to variational formulation of Dirac dynamics.

We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class $\mathcal{C}$ of Fujiki. We give a Hodge-theoretical proof of the characterization of solvmanifolds in class $\mathcal{C}$ of Fujiki, first proven by D.…

The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H\subset G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and an explicit g…

Generalizes cohomological obstruction for quasiregular ellipticity.

In this work we introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction we obtain both positive and negative results on the existence of symplectic structures on a larg…

New exact sequence links cohomology, automorphisms, and extensions of symmetric quandles.

We answer the natural question: when are a regular Poisson structure along with a complex structure transverse to its symplectic leaves induced by generalized complex structure? The leafwise symplectic form and transverse complex structure determine an obstruction class in a certain cohomology, which vanishes if and on…

This research studies the smoothness of moduli spaces of self-dual contact instantons on Sasakian manifolds.

Study cohomology dimensions jumping in complex manifold deformations.