On the LS-category and topological complexity of projective product spaces

Fişekci, Seher; Vandembroucq, Lucile

doi:10.48550/arxiv.2012.04777

Cited by 1 publication

(2 citation statements)

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“…We accomplish this by constructing an explicit motion planning on these spaces. In this context, the advantages of more direct methods in the digital sense provide the results in [16] apart from requiring cohomological operational lower bound properties.…”

Section: Discussionmentioning

confidence: 99%

“…The topological complexity and some bounds of these spaces have been initiated in [17]. The improvement of this study to finalize the estimating problem about the topological complexity and the Lusternik-Schnirelmann category of projective product spaces has been included in [16]. Fişekci and Vandembroucq compute the Lusternik-Schnirelmann category of PPS and determine an exact value of the topological complexity for some cases.…”

Section: Introductionmentioning

confidence: 99%

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Explicit motion planning in digital projective product spaces

Fişekci¹,

Karaca²

2021

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We introduce the digital projective product spaces based on Davis' projective product spaces. We determine an upper bound for the digital LS-category of the digital projective product spaces. In addition, we obtain an upper bound for the digital topological complexity of these spaces. We prove the relation between the digital topological complexity of the digital projective product spaces and sum of the digital topological complexity of the digital projective space by associating with the first digital sphere and the digital topological complexity of the remaining digital spheres through an explicit motion planning construction, which shows digital perspective validity of the results given by S. Fişekci and L. Vandembroucq.We apply our outcomes on specific spaces in order to be more clear.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%