seriously disabled Posted April 7, 2010 Share Posted April 7, 2010 In algebraic topology there is something called a chain complex. http://en.wikipedia.org/wiki/Chain_complex My question is: Why is the composition of any two consecutive maps [math]d_n \cdot d_{n+1}[/math] equal zero? Link to comment Share on other sites More sharing options...
ajb Posted April 10, 2010 Share Posted April 10, 2010 You want [math]Im(d_{n+1}) \subseteq Ker(d_{n})[/math] so that the homology groups are well defined. This follows from the nilpotent property of the operator. Link to comment Share on other sites More sharing options...
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