ベッチ数
}
コンパクトな単純リー群のポアンカレ多項式は、
P S U ( n + 1 ) ( x ) = ( 1 + x 3 ) ( 1 + x 5 ) . . . ( 1 + x 2 n + 1 ) {\displaystyle P_{SU(n+1)_{}}(x)=(1+x^{3})(1+x^{5})...(1+x^{2n+1})}
P S O ( 2 n + 1 ) ( x ) = ( 1 + x 3 ) ( 1 + x 7 ) . . . ( 1 + x 4 n − 1 ) {\displaystyle P_{SO(2n+1)_{}}(x)=(1+x^{3})(1+x^{7})...(1+x^{4n-1})}
P S p ( n ) ( x ) = ( 1 + x 3 ) ( 1 + x 7 ) . . . ( 1 + x 4 n − 1 ) {\displaystyle P_{Sp(n)_{}}(x)=(1+x^{3})(1+x^{7})...(1+x^{4n-1})}
P S O ( 2 n ) ( x ) = ( 1 + x 2 n − 1 ) ( 1 + x 3 ) ( 1 + x 7 ) . . . ( 1 + x 4 n − 5 ) {\displaystyle P_{SO(2n)_{}}(x)=(1+x^{2n-1})(1+x^{3})(1+x^{7})...(1+x^{4n-5})}
P G 2 ( x ) = ( 1 + x 3 ) ( 1 + x 11 ) {\displaystyle P_{G_{2}}(x)=(1+x^{3})(1+x^{11})}