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- W2897511391 abstract "This paper describes a mechanism by which a traversally generic flow $v$ on a smooth connected manifold $X$ with boundary produces a compact $CW$-complex $mathcal T(v)$, which is homotopy equivalent to $X$ and such that $X$ embeds in $mathcal T(v)times mathbf R$. The $CW$-complex $mathcal T(v)$ captures some residual information about the smooth structure on $X$ (such as the stable tangent bundle of $X$). Moreover, $mathcal T(v)$ is obtained from a simplicial emph{origami map} $O: D^n to mathcal T(v)$, whose source space is a disk $D^n subset partial X$ of dimension $n = dim(X) -1$. The fibers of $O$ have the cardinality $(n+1)$ at most. The knowledge of the map $O$, together with the restriction to $D^n$ of a Lyapunov function $f:X to mathbf R$ for $v$, make it possible to reconstruct the topological type of the pair $(X, mathcal F(v))$, were $mathcal F(v)$ is the $1$-foliation, generated by $v$. This fact motivates the use of holography in the title." @default.
- W2897511391 created "2018-10-26" @default.
- W2897511391 creator A5021465332 @default.
- W2897511391 date "2018-10-06" @default.
- W2897511391 modified "2023-09-27" @default.
- W2897511391 title "The Disk-Based Origami Theorem and a Glimpse of Holography for Traversing Flows" @default.
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