Sequential parametrized topological complexity of sphere bundles Article Swipe
Michael Färber
,
Amit Kumar Paul
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1007/s40879-024-00766-w
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1007/s40879-024-00766-w
Autonomous motion of a system (robot) is controlled by a motion planning algorithm. A sequential parametrized motion planning algorithm [10] works under variable external conditions and generates continuous motions of the system to attain the prescribed sequence of states at prescribed moments of time. Topological complexity of such algorithms measures their structure and discontinuities. Information about states of the system consistent with states of the external conditions is described by a fibration $$p:E\rightarrow B$$ where the base B parametrizes the external conditions and each fibre $$p^{-1}(b)$$ is the configuration space of the system constrained by external conditions $$b\in B$$ ; more detail on this approach is given below. Our main goal in this paper is to study the sequential topological complexity of sphere bundles $$\dot{\xi }:\dot{E}\rightarrow B$$ ; in other words we study “parametrized families of spheres” and sequential parametrized motion planning algorithms for such bundles. We use the Euler and Stiefel–Whitney characteristic classes to obtain lower bounds on the topological complexity. We illustrate our results by many explicit examples. Some related results for the special case $$r=2$$ were described earlier in [13].
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- article
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- en
- Landing Page
- https://doi.org/10.1007/s40879-024-00766-w
- OA Status
- hybrid
- Cited By
- 1
- References
- 18
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https://openalex.org/W4402825957Canonical identifier for this work in OpenAlex
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https://doi.org/10.1007/s40879-024-00766-wDigital Object Identifier
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Sequential parametrized topological complexity of sphere bundlesWork title
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articleOpenAlex work type
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enPrimary language
- Publication year
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2024Year of publication
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2024-09-25Full publication date if available
- Authors
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Michael Färber, Amit Kumar PaulList of authors in order
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https://doi.org/10.1007/s40879-024-00766-wPublisher landing page
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YesWhether a free full text is available
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hybridOpen access status per OpenAlex
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https://doi.org/10.1007/s40879-024-00766-wDirect OA link when available
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Topological complexity, Topology (electrical circuits), Mathematics, Pure mathematics, Computer science, CombinatoricsTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2025: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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