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Smooth structures on pseudomanifolds with isolated conical singularities

icon-email Hông Vân Lê , Petr Somberg , Jiří Vanžura

Abstract

In this note we introduce the notion of a smooth structure on a conical pseudomanifold M in terms of C∞-rings of smooth functions on M. For a finitely generated smooth structure C∞(M) we introduce the notion of the Nash tangent bundle, the Zariski tangent bundle, the tangent bundle of M, and the notion of characteristic classes of M. We prove the vanishing of a Nash vector field at a singular point for a special class of Euclidean smooth structures on M. We introduce the notion of a conical symplectic form on M and show that it is smooth with respect to a Euclidean smooth structure on M. If a conical symplectic structure is also smooth with respect to a compatible Poisson smooth structure C∞(M), we show that its Brylinski–Poisson homology groups coincide with the de Rham homology groups of M. We show nontrivial examples of these smooth conical symplectic-Poisson pseudomanifolds.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      • 20. view::22404baedef17ea59e3ac1e1ef4f69087a37cb5d:31
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
      Backtrace
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