In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954.
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Thom定理：低維閉流形是高維流形的邊緣（映射的像）那麼低維閉流形的不變量定義為高維流形的指標和龐特裏亞金類的多項式。Hirzebruch通過托姆配邊定理證明瞭流形的指標是龐特裏亞金類的多項式的假設，然後就得到瞭高維的黎曼羅赫定理。格羅滕迪剋代數化瞭這個定理得到瞭簇間的黎曼羅赫定理（簇間映射分解為投影和嵌入的形變）。博特和阿蒂亞通過整性概念的引導藉鑒瞭Lefschetz 復解析流形不動點定理，得到瞭李群外爾特徵公式
评分Thom定理：低維閉流形是高維流形的邊緣（映射的像）那麼低維閉流形的不變量定義為高維流形的指標和龐特裏亞金類的多項式。Hirzebruch通過托姆配邊定理證明瞭流形的指標是龐特裏亞金類的多項式的假設，然後就得到瞭高維的黎曼羅赫定理。格羅滕迪剋代數化瞭這個定理得到瞭簇間的黎曼羅赫定理（簇間映射分解為投影和嵌入的形變）。博特和阿蒂亞通過整性概念的引導藉鑒瞭Lefschetz 復解析流形不動點定理，得到瞭李群外爾特徵公式
评分Thom定理：低維閉流形是高維流形的邊緣（映射的像）那麼低維閉流形的不變量定義為高維流形的指標和龐特裏亞金類的多項式。Hirzebruch通過托姆配邊定理證明瞭流形的指標是龐特裏亞金類的多項式的假設，然後就得到瞭高維的黎曼羅赫定理。格羅滕迪剋代數化瞭這個定理得到瞭簇間的黎曼羅赫定理（簇間映射分解為投影和嵌入的形變）。博特和阿蒂亞通過整性概念的引導藉鑒瞭Lefschetz 復解析流形不動點定理，得到瞭李群外爾特徵公式
评分Thom定理：低維閉流形是高維流形的邊緣（映射的像）那麼低維閉流形的不變量定義為高維流形的指標和龐特裏亞金類的多項式。Hirzebruch通過托姆配邊定理證明瞭流形的指標是龐特裏亞金類的多項式的假設，然後就得到瞭高維的黎曼羅赫定理。格羅滕迪剋代數化瞭這個定理得到瞭簇間的黎曼羅赫定理（簇間映射分解為投影和嵌入的形變）。博特和阿蒂亞通過整性概念的引導藉鑒瞭Lefschetz 復解析流形不動點定理，得到瞭李群外爾特徵公式
评分Thom定理：低維閉流形是高維流形的邊緣（映射的像）那麼低維閉流形的不變量定義為高維流形的指標和龐特裏亞金類的多項式。Hirzebruch通過托姆配邊定理證明瞭流形的指標是龐特裏亞金類的多項式的假設，然後就得到瞭高維的黎曼羅赫定理。格羅滕迪剋代數化瞭這個定理得到瞭簇間的黎曼羅赫定理（簇間映射分解為投影和嵌入的形變）。博特和阿蒂亞通過整性概念的引導藉鑒瞭Lefschetz 復解析流形不動點定理，得到瞭李群外爾特徵公式
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