Question

Compute the simplicial Betti numbers of the simplicial complex K = {1,2,3,4,5,6,7,(1,2),(2,3),(1,3),(1,4),(3,4),(2,4),(2,5),(5,6),(6,7),(5,7), (1,2,3),(1,2,4),(2,3,4),(1,3,4)}, a “zipped up tent with a torn flag”. Here you can think of the lists in parentheses as my choices for the orientations of corresponding simplices.

Answer 1

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Given, Simplical complex K={1,2,3,4,5,6,7. (1,2),(2,3)(1,3) (1,9%8, 4),(2,4). (2,9 (67(5.4 (51) (42,3)[1,2,4) (2,3,4) (43, 4) betti number Know number We must of zero complex, number of For calculating I complee and number of 2-complex betti number for k is equal to - Number of zero complex 1- complex of zero complex-number of 1 & number hamber of a complex 7- 10+ 4 -Il- 10 So Betli number is I/ 1