arXiv research

Geometric model for Hodge filtered complex cobordism constructed.

Paper constructs Thom-Smale complex using instantons from Morse functions.

In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.

We construct the first examples of non-Kähler complex structures on $R^4$. These complex surfaces have some analogies with the complex structures constructed in early Fifties by Calabi and Eckmann on the products of two odd-dimensional spheres. However, our construction is quite different from that of Calabi and Eckman…

We construct a natural generalized complex structure on the total space of any bundle endowed with a Chern connection and whose typical fibre is a homogeneous symplectic manifold. This extends known constructions of generalized complex structures on Lie groups and leads to natural examples of holomorphic maps between g…

Paper proves uniqueness of a complex construction.

Alternative construction of Rumin complex on Lie groups.

We investigate Lie algebras endowed with a complex symplectic structure and develop a method, called \emph{complex symplectic oxidation}, to construct certain complex symplectic Lie algebras of dimension $4n+4$ from those of dimension $4n$. We specialize this construction to the nilpotent case and apply complex symplec…

New method constructs Birkhoff sections for pseudo-Anosov flows with controlled complexity.

Synthetic construction of 3D complex bases.

Researchers match complex affine structures in mirror constructions.

Constructs simplified or complexified simplicial complexes.

This note constructs complex structures on specific isoparametric hypersurfaces.

In the previous papers \cite{L1, L2} the author constructed Mabuchi and Aubin-Yau functionals over any complex surfaces and three-folds, respectively. Using the method in \cite{L2}, we construct those functionals over any complex manifolds of the complex dimension bigger than or equal to 2.

Constructs explicit harmonic functions and morphisms on complex and quaternionic Grassmannians.

The paper constructs instanton complexes on stratified pseudomanifolds.

The moment-angle complex Z_K is cell complex with a torus action constructed from a finite simplicial complex K. When this construction is applied to a triangulated sphere K or, in particular, to the boundary of a simplicial polytope, the result is a manifold. Moment-angle manifolds and complexes are central objects in…

New construction reduces Vietoris-Rips complex construction time.

New topological realization of Kontsevich graph complex for large dimensions.

Method uses network biology to construct gene expression models for cancer.

New $t$-LC triangulated manifolds are exponentially many.

Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven fashion, (twisted) generalized complex structures are constructed on a myriad of four-…

The Novikov complex of a circle-valued Morse function is constructed algebraically from the Morse-Smale complex of the restriction to a fundamental domain of the real-valued Morse function on the pullback infinite cyclic cover.

The paper constructs discrete Hessian and divdiv complexes on triangulations and proves their cohomology isomorphic to continuous versions.

Risk diversification is one of the dominant concerns for portfolio managers. Various portfolio constructions have been proposed to minimize the risk of the portfolio under some constrains including expected returns. We propose a portfolio construction method that incorporates the complex valued principal component anal…

New group constructed from cube complex properties.

Proposes CXNs for neural network computations on cell complexes.

The paper constructs Morse complexes for orbifolds and shows their homologies are orbifold invariants.

Given a compact Hermitian complex space with isolated singular points, we construct a Dolbeault-type Hilbert complex whose cohomology is isomorphic to the cohomology of the structure sheaf. We show that the corresponding K-homology class coincides with the one constructed by Baum-Fulton-MacPherson.

The study constructs minimal submanifolds in complex and quaternionic projective spaces.

We construct families of trivial $2$-knots $K_i$ in $\mathbb{R}^4$ such that the maximal complexity of $2$-knots in any isotopy connecting $K_i$ with the standard unknot grows faster than a tower of exponentials of any fixed height of the complexity of $K_i$. Here we can either construct $K_i$ as smooth embeddings and …

Sphere-bases for simplicial and cubical complexes are constructed and analyzed.

We describe a series of complexes that relate to the braid groups as the matching complexes relate to the symmetric groups. A modified construction applies as well to other complexes based on edge sets in graphs. We show that our constructions will yield Cohen-Macauley complexes provided the underlying complexes are Co…

In this paper, we define a relative Morse complex for manifold with boundary using the handlebody decomposition of the manifold. We prove that the homology of the relative Morse complex is isomorphic to the relative singular homology. Furthermore, we construct $A_\infty$-category structure on the relative Morse complex…

The paper constructs exotic knotted surfaces and curves in 4-manifolds.

Explicitly constructed 3XOR instances hard for Sum-of-Squares hierarchy.

New complex non-Kähler manifolds with specific properties are constructed.

Constructs a new geometric structure on surfaces to generalize Teichmüller theory.

New complexes refine multicomplexes for subRiemannian geometry.

New complex structures found on tangent bundles of Lie groups.

We extend the construction of the BFV-complex of a coisotropic submanifold from the Poisson setting to the Jacobi setting. In particular, our construction applies in the contact and l.c.s. settings. The BFV-complex of a coisotropic submanifold $S$ controls the coisotropic deformation problem of $S$ under both Hamiltoni…

The paper constructs a complex for the Dirac operator in 4 dimensions.

New symplectic 4-manifolds with non-negative signatures are constructed using complex surfaces and quotients.

We introduce the notion of a conformally Fedosov structure and construct an associated Cartan connection. When an appropriate curvature vanishes, this allows us to construct a family of natural differential complexes akin to the BGG complexes from parabolic geometry.

Constructs Morse homology for complex algebraic varieties.

The study classifies complex symplectic structures on 4D Lie algebras and constructs hypersymplectic structures.

Lecture notes on BGG complexes using Lie groups and algebras.

A natural map from Lawson homology to Deligne cohomology groups for smooth complex projective varieties is constructed by using the Harvey-Lawson spark complexes. We also compare this to Abel-Jacobi type constructions by others.