On the push-out space

Morteza Fathy; Morteza Faghfouri

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arXiv · 1304.4924

On the push-out space

Morteza Fathy·Morteza Faghfouri

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Abstract

Let $f:M^m\longrightarrow \Bbb R^{m+k}$ be an immersion where $M$ is a smooth connected $m$-dimensional manifold without boundary. Then we construct a subspace $\Omega(f)$ of $ \mathbb{R}^k$, namely push-out space. which corresponds to a set of embedded manifolds which are either parallel to $ f $, tubes around $ f $ or, ingeneral, partial tubes around $ f $. This space is invariant under the action of the normal holonomy group, $\mathcal{H}ol(f)$. Moreover, we construct geometrically some examples for normal holonomy group and push-out space in ${\Bbb R}^3$.These examples will show that properties of push-out space that are proved in the case $\mathcal{H}ol(f)$ is trivial, is not true in general.

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Morteza Fathy, Morteza Faghfouri. 2013-04-17. On the push-out space. https://arxiv.org/abs/1304.4924

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