An explicit formula for the cup-length of the rotation group

Korbaš, Július

doi:10.36045/bbms/1506477684

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It Was Shown By Farber In [Far03 Theorem 7] That1

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2019

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“…Note that Korbaš formulates his result only for the case F 2 = Z 2 in [Kor17], but his proof, which depends only on the combinatorial structure of the cohomology ring, generalizes to arbitrary fields of characteristic two. Computing the first values of this formula particulary provides cl F 2 (SO(2)) = 1, cl F 2 (SO(3)) = 3, cl F 2 (SO(4)) = 4, cl F 2 (SO(5)) = 8, .…”

Section: It Was Shown By Farber In [Far03 Theorem 7] Thatmentioning

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: It Was Shown By Farber In [Far03 Theorem 7] Thatmentioning

confidence: 99%