Manifolds with small topological complexity

Pavešić, Petar

doi:10.48550/arxiv.2011.13754

Cited by 1 publication

(1 citation statement)

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“…The reader can easily see that this puts strong restrictions on the cup product structures of M. A more sophisticated analysis of the cohomological restrictions for closed oriented manifolds whose TC is at most two was carried out by P. Pavešić in [69]. In the following result, we use the usual convention in graded rings that x i shall always denote a generator of degree i.…”

Section: Theorem 14 Let P : E → B Be a Fibration Let A Be An Abelian ...mentioning

confidence: 99%

Oriented robot motion planning in Riemannian manifolds

Mescher

2019

Topology and its Applications

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We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we study the topological complexity of oriented frame bundles, derive an upper bound for this invariant and certain lower bounds from cup length computations. In particular, we show that for large classes of oriented manifolds, e.g. for spin manifolds, the topological complexity of the oriented frame bundle is bounded from below by the dimension of the base manifold.Date: February 27, 2019.In the following we consider the spaces S(M) and S n as spaces with free Z 2 -actions given by the deck transformation actions of q M and q n , resp. Definition 5.7. a) Given a spin manifold M we let i(M) denote the biggest integer k ∈ N for which there exists a continuous Z 2 -equivariant map f : S k → S(M) with respect to the antipodal involution on S k .

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Section: Theorem 14 Let P : E → B Be a Fibration Let A Be An Abelian ...mentioning

confidence: 99%