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Titlebook: Algebraic Topology and Related Topics; Mahender Singh,Yongjin Song,Jie Wu Conference proceedings 2019 Springer Nature Singapore Pte Ltd. 2

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Arc Shift Number for Some Virtual Knots,In this paper, we compute the arc shift number for some classes of virtual knots and show that for every positive integer ., there exist infinitely many virtual knots with arc shift number .. We conclude the paper by computing the arc shift number for an infinite family of virtual knots with virtual bridge index one.
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-Groups of Stunted Complex and Quaternionic Projective Spaces,In this note, we compute .-groups of the stunted projective space ., where . or .. We also prove some non-sectioning results of certain maps of stunted complex projective spaces into certain quotients.
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Springer Nature Singapore Pte Ltd. 2019
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https://doi.org/10.1007/978-981-15-2140-9Borsuk–Ulam theorem is used to show that, if ., then the covering dimension of the space of vectors . such that . is at least .. It is shown, further, that there exists such a map . for which this zero-set has covering dimension equal to ..
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https://doi.org/10.1007/978-981-15-2140-9h the .-primary homotopy exponents of spheres . and ., respectively. We further study the exponent problem when . is a space with the homotopy type of . for a homotopy .-sphere ., the complex projective space . for . or the quaternionic projective space . for ..
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