Corrigendum: On Kontsevich's characteristic classes for higher‐dimensional sphere bundles II: Higher classes

Watanabe, Tadayuki

doi:10.1112/topo.12220

Journal of Topology

2022

DOI: 10.1112/topo.12220

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Corrigendum: On Kontsevich's characteristic classes for higher‐dimensional sphere bundles II: Higher classes

Tadayuki Watanabe

Abstract: We fix an error in the proof of Theorem 6.1(ii) in Watanabe (J. Topol. 2 (2009), no. 3, 624-660), and extend the main result of that paper to all odd dimensions at least 5.

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2023

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Families of diffeomorphisms and concordances detected by trivalent graphs

Botvinnik

Watanabe

2023

Journal of Topology

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We study families of diffeomorphisms detected by trivalent graphs via the Kontsevich classes. We specify some recent results and constructions of the second named author to show that those non-trivial elements in homotopy groups 𝜋 * (𝐵Dif f 𝜕 (𝐷 𝑑 )) ⊗ ℚ are lifted to homotopy groups of the moduli space of ℎ-cobordisms 𝜋 * (𝐵Dif f ⊔ (𝐷 𝑑 × 𝐼)) ⊗ ℚ. As a geometrical application, we show that those elements in 𝜋 * (𝐵Dif f 𝜕 (𝐷 𝑑 )) ⊗ ℚ for 𝑑 ⩾ 4 are also lifted to the rational homotopy groups 𝜋 * (ℳ 𝗉𝗌𝖼 𝜕 (𝐷 𝑑 ) ℎ 0 ) ⊗ ℚ of the moduli space of positive scalar curvature metrics. Moreover, we show that the same elements come from the homotopy groups 𝜋 * (ℳ 𝗉𝗌𝖼 ⊔ (𝐷 𝑑 × 𝐼; g 0 ) ℎ 0 ) ⊗ ℚ of moduli space of concordances of positive scalar curvature metrics on 𝐷 𝑑 with fixed-round metric ℎ 0 on the boundary 𝑆 𝑑−1 .

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Families of diffeomorphisms and concordances detected by trivalent graphs

Botvinnik

Watanabe

2023

Journal of Topology

Self Cite

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Corrigendum: On Kontsevich's characteristic classes for higher‐dimensional sphere bundles II: Higher classes

Abstract: We fix an error in the proof of Theorem 6.1(ii) in Watanabe (J. Topol. 2 (2009), no. 3, 624-660), and extend the main result of that paper to all odd dimensions at least 5.

Cited by 1 publication

References 5 publications

Families of diffeomorphisms and concordances detected by trivalent graphs

Families of diffeomorphisms and concordances detected by trivalent graphs

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