It is known since 1954 that every 3-manifold bounds a 4-manifold. Thus, for instance, every 3-manifold has a surgery diagram. There are several proofs of this fact, including constructive proofs, but there has been little attention to the complexity of the 4-manifold produced. Given a 3-manifold M of complexity n, we show how to construct a 4-manifold bounded by M of complexity O(n). Here we me...

It is known since 1954 that every 3-manifold bounds a 4-manifold. Thus, for instance, every 3-manifold has a surgery diagram. There are several proofs of this fact, including constructive proofs, but there has been little attention to the complexity of the 4-manifold produced. Given a 3-manifold M of complexity n, we show how to construct a 4-manifold bounded by M of complexity O(n). Here we me...

This paper gives an attempt to explore the manifold in the label space for multi-label learning. Traditional label space is logical, where no manifold exists. In order to study the label manifold, the label space should be extended to a Euclidean space. However, the label manifold is not explicitly available from the training examples. Fortunately, according to the smoothness assumption that th...

‎using nehari manifold methods and mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-kirchhoff-type system are established.

on a finsler manifold, we define conformal vector fields and their complete lifts and prove that incertain conditions they are homothetic.

in 4D Orthogonal Pseudo-Polytopes Ricardo Pérez Aguila Antonio Aguilera Ramírez Centro de Investigación en Tecnologías de Información y Automatización (CENTIA) Universidad de las Américas – Puebla (UDLAP) Ex-Hacienda Santa Catarina Mártir. Phone: +52 (222) 229-2664 México 72820, Cholula, Puebla. [email protected] [email protected] ABSTRACT This article presents our experimental result...

An exact manifold with pseudoconvex boundary (PC manifold, for short) is a compact complex manifold X, which admits a strictly pluri-subharmonic Morse function ψ, such that the set of maximum points of ψ coincides with the boundary ∂X. We prefer the term PC manifold, since the combination of words “compact Stein manifold” is likely to precipitate heart palpitations in some mathematicians. Such ...

This paper addresses the numerical estimation of the principal curvature of pattern transformation manifolds. When a visual pattern undergoes a geometric transformation, it forms a (sub)manifold in the ambient space, which is usually called the transformation manifold. The manifold curvature is an important property characterizing the manifold geometry, with several applications in manifold lea...

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.