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- W2499123406 abstract "We present an efficient algorithm for the construction of a basis of $H_2(overline{Omega},partialOmega;mathbb Z)$ via the Poincare--Lefschetz duality theorem. Denoting by $g$ the first Betti number of $overline Omega$ the idea is to find, first $g$ different $1$-boundaries of $overline{Omega}$ with supports contained in $partialOmega$ whose homology classes in $mathbb R^3 setminus Omega$ form a basis of $H_1(mathbb R^3 setminus Omega;mathbb Z)$, and then to construct in $overline{Omega}$ a homological Seifert surface of each one of these $1$-boundaries. The Poincare--Lefschetz duality theorem ensures that the relative homology classes of these homological Seifert surfaces in $overlineOmega$ modulo $partialOmega$ form a basis of $H_2(overlineOmega,partialOmega;mathbb Z)$. We devise a simply procedure for the construction of the required set of $1$-boundaries of $overline{Omega}$ that, combined with a fast algorithm for the construction of homological Seifert surfaces, allows the efficient computation of a basis of $H_2(overline{Omega},partialOmega;mathbb Z)$ via this very natural geometrical approach. Some numerical experiments show the efficiency of the method and its performance comparing with other algorithms." @default.
- W2499123406 created "2016-08-23" @default.
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- W2499123406 date "2016-07-18" @default.
- W2499123406 modified "2023-10-02" @default.
- W2499123406 title "Geometric construction of bases of $H_2(overlineOmega, partialOmega, mathbb{Z})$" @default.
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