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Since 1962, the NVR has been maintained and published by the NAVSEA Shipbuilding Support Office (NAVSHIPSO) of the Naval Sea Systems Command. Referred to by Congress in the statutes of 10 U.S.C. §§ 8674–8678, the NVR is maintained as directed by U.S. Navy Regulations, Article 0406, of September 14, 1990.
where H 0 (X,A) is the group A(X) of global sections of A on X. For example, if the group H 1 (X,A) is zero, then this exact sequence implies that every global section of C lifts to a global section of B. More broadly, the exact sequence makes knowledge of higher cohomology groups a fundamental tool in aiming to understand sections of sheaves.
NVR, Inc. is an American company engaged in home construction headquartered in Reston, Virginia. It also operates a mortgage banking and title services business. The company primarily operates on the East Coast of the United States , but its operations encompass 14 states as well as Washington, D.C.
Let X be a topological space and A, B be two subspaces whose interiors cover X. (The interiors of A and B need not be disjoint.) The Mayer–Vietoris sequence in singular homology for the triad (X, A, B) is a long exact sequence relating the singular homology groups (with coefficient group the integers Z) of the spaces X, A, B, and the intersection A∩B. [8]
When n=1, the formula becomes =,. According to the Hodge theorem , h 0 , 1 = h 1 , 0 {\displaystyle h^{0,1}=h^{1,0}} . Consequently h 0 , 1 = h 1 ( X ) / 2 = g {\displaystyle h^{0,1}=h^{1}(X)/2=g} , where g is the usual (topological) meaning of genus of a surface, so the definitions are compatible.
called the nth homology group of X. The elements of H n (X) are called homology classes. Each homology class is an equivalence class over cycles and two cycles in the same homology class are said to be homologous. [6] A chain complex is said to be exact if the image of the (n+1)th map is always equal to the kernel of the nth map.
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