arXiv research

New quantum code lacks sparse lift.

Simple lifts of non-simple curves on surfaces.

We define an integer graded symplectic Floer cohomology and a spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopies. Such an integer graded Floer cohomology is an integral lifting of the usual Floer-Oh cohomology with $Z_{\Si (L)}$ grading. As one of applications of the sp…

Researchers lift knot coloring polynomial to Habiro ring.

Homomorphism from braid groups to Steinberg groups defined.

The paper proves every closed curve on a bouquet of circles lifts to finite covers.

We give an explicit description and calculate the dimension of the vector space of linear natural liftings of $p$-forms on $n$-dimensional manifolds $M$ to $q$-forms on $T^{{\mathbb D}^r_k}M$, where ${\mathbb D}^r_k$ is the Weil algebra of $r$-jets at 0 of smooth functions ${\mathbb R}^k\longrightarrow{\mathbb R}$, for…

New method computes link invariants using special Whitney towers.

We provide linear lower bounds for $f_ρ(L)$, the smallest integer so that every curve on a fixed hyperbolic surface $(S,ρ)$ of length at most $L$ lifts to a simple curve on a cover of degree at most $f_ρ(L)$. This bound is independent of hyperbolic structure $ρ$, and improves on a recent bound of Gupta-Kapovich. When $…

Simplified proof for a theorem about graphs.

New invariants lift Milnor invariants for 3-component links.

We introduce a gauge-theoretic integer lift of the Rohlin invariant of a smooth 4-manifold X with the homology of $S^1 \times S^3$. The invariant has two terms; one is a count of solutions to the Seiberg-Witten equations on X, and the other is essentially the index of the Dirac operator on a non-compact manifold with e…

We lift the characteristic-2 totally twisted Khovanov homology of Roberts and Jaeger to a theory with integer coefficients. The result is a complex computing reduced odd Khovanov homology for knots. This complex is equivalent to a spanning-tree complex whose differential is explicit modulo a sign ambiguity coming from …

The cohomology ring with coefficients in $\Z_p$, where $p$ is a prime integer, of a Seifert manifold $M$, orientable or not orientable is obtained from a simplicial decomposition of $M$. Many choices must be made before applying Alexander-Whitney formula to get the cup-products. The most difficult choices are those of …

We develop a method of calculation for the symplectic Floer homology of composite knots. The symplectic Floer homology of knots defined in \cite{li} naturally admits an integer graded lifting, and it formulates a filtration and induced spectral sequence. Such a spectral sequence converges to the symplectic homology of …

For every finite collection of curves on a surface, we define an associated (semi-)norm on the first homology group of the surface. The unit ball of the dual norm is the convex hull of its integer points. We give an interpretation of these points in terms of certain coorientations of the original collection of curves. …

Symmetric function $L_{M,N}$ lifts torus link homology.

We define an integer graded symplectic Floer cohomology and a Fintushel-Stern type spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopes. The Z-graded symplectic Floer cohomology is an integral lifting of the usual Z_Sigma(L)-graded Floer-Oh cohomology. We prove the Kunneth…

In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation that realizes these invariants. The current article is restricted to surfaces wi…

Proves M-theory anomaly cancellation on nonorientable manifolds.

Existence and rigidity results for lifts in Carnot groups.

Study lift metrics and connections on tangent bundles of Riemannian manifolds.

Proves curvature bounds for submanifolds in negatively curved spaces.

In this paper, we define a complete lift for semisprays. If $S$ is a semispray on a manifold $M$, its complete lift is a new semispray $S^c$ on $TM$. The motivation for this lift is two-fold: First, geodesics for $S^c$ correspond to the Jacobi fields for $S$, and second, this complete lift generalizes and unifies previ…

Unified approach to constructing integrable systems using Stäckel lifts.

Geometric structures are lifted to higher tangent bundles preserving statistical properties.

The article classifies liftings of connections on differential manifolds for geodesic modeling.

Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.

In the present paper, we study complete and vertical lifts of tensor fields from a smooth manifold $M$ to its Weil bundle $T^A M$ defined by a Frobenius Weil algebra $A$. For a Poisson manifold $(M,w)$, we show that the complete lift $w^C$ and the vertical lift $w^V$ of the Poisson tensor $w$ are Poisson tensors on $T^…

Study lifts plane mappings to Heisenberg group.

The paper lifts spherical Morse functions to immersions and embeddings.

In this paper we continue to study equivariant pencil liftings and differential operators on the algebra of densities. We emphasize the role that the geometry of the extended manifold plays. Firstly we consider basic examples. We give a projective line of diff($M$)-equivariant pencil liftings for first order operators,…

Study covers of sphere with homeomorphisms lifting property.

This paper studies surfaces with a special lift property.

The canonical trace and the Wodzicki residue on classical pseudodifferential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral $ζ$-invariants using lifted …

The paper constructs Sasakian lifts from Kähler manifolds and studies their properties.

The paper discusses symplectic lifts for actions on Lagrangian fibrations.

Criteria for lifting manifold diffeomorphisms to vector bundle automorphisms.

Characterizes sphere covers with lifted homeomorphisms.

This paper extends braid lifting to coloured braid groupoids for all simple disc covers.

We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This generalizes the complete lift defined by I.Sato and the horizontal lift introduced by K.Yano and S.Ishihara. We study some geometric properties of this lift and its compatibility with symplectic …

Curious examples of lifting spaces not as inverse limits of covering spaces.

Defines lift of partial cohomological field theories and finds new bi-Hamiltonian structures.

Fenchel lifted networks improve neural network training without performance loss.

In Finsler geometry the complete lift vector fields have distinguished geometric significance. For example a vector field on a Finsler manifold is said to be conformal if its complete lift is conformal in usual sense. In this work we define a new Riemannian or Pseudo-Riemannian metric on TM derived from a Finsler metri…

Proves harmonicity equivalence on manifold metrics.

The Eisenhart lift connects Hamiltonian systems to geodesics in pp-wave spacetimes.

Survey of twistor lifts of surfaces in 4-dimensional spaces.