1701046455
1701046456
1701046457
1701046458
1701046459
这里n=dimK.
1701046460
1701046461
以后会看到,一般地dq与βq不一定相同.
1701046462
1701046463
习 题
1701046464
1701046465
1.若K=K1∪K2,K0=K1∩K2是r维的,则
1701046466
1701046467
1701046468
∀q>r+1.
1701046469
1701046470
2.若K=K1∪K2,K0=K1∩K2是一个顶点,则
1701046471
1701046472
1701046473
∀q>0.
1701046474
1701046475
3.设K=K1∪K2,K0=K1∩K2非空,试证明
1701046476
1701046477
(1)若K0连通,则∀z∈Z1(K),存在zi∈Z1(Ki),i=1,2,使得z=z1+z2;
1701046478
1701046479
(2)若Hq-1(K0)=0,则∀z∈Zq(K),存在zi∈Zq(Ki),i=1,2,使得z=z1+z2;
1701046480
1701046481
(3)若Hq(K0)=0,zi∈Zq(Ki)(i=1,2)使z1+z2在K中同调于0,则zi在Ki中同调于0,i=1,2.
1701046482
1701046483
4.设K=K1∪K2,K0=K1∩K2是零调的,即
1701046484
1701046485
1701046486
1701046487
1701046488
证明
1701046489
1701046490
1701046491
∀q≠0.
1701046492
1701046493
5.利用Euler-Poincaré公式证明树的顶点数比1维单形数大1.
1701046494
1701046495
6.详细写出关于以域G为系数群的Euler-Poincaré公式的证明.
1701046496
1701046497
7.设K是连通复形,G为交换群,证明
1701046498
1701046499
1701046500
1701046501
1701046503
§4 计算同调群的实例
1701046504
[
上一页 ]
[ :1.701046455e+09 ]
[
下一页 ]