On the push-out space
Morteza Fathy, Morteza Faghfouri

TL;DR
This paper introduces the concept of push-out space for immersions of manifolds into Euclidean space, exploring its properties, invariance under normal holonomy, and providing geometric examples illustrating its behavior.
Contribution
It defines the push-out space for manifold immersions, studies its invariance under normal holonomy, and constructs geometric examples demonstrating its properties.
Findings
Push-out space is invariant under the normal holonomy group.
Properties of push-out space differ when the holonomy group is non-trivial.
Examples in ${ m I ext{-}R}^3$ illustrate these properties.
Abstract
Let be an immersion where is a smooth connected -dimensional manifold without boundary. Then we construct a subspace of , namely push-out space. which corresponds to a set of embedded manifolds which are either parallel to , tubes around or, ingeneral, partial tubes around . This space is invariant under the action of the normal holonomy group, . Moreover, we construct geometrically some examples for normal holonomy group and push-out space in .These examples will show that properties of push-out space that are proved in the case is trivial, is not true in general.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds
