Suppose all even-indexed linear transformations in the chain
complexC•are 0 transformations and all odd-indexed transformations
are bijections.Compute...
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Advance Math
Suppose all even-indexed linear transformations in the chaincomplexC•are 0 transformations and all odd-indexed transformationsare bijections.Compute the homology of this complex
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The definition of a Clinear functionimpliesthat lz az bz so liz iaz bz Therefore liz ilz if and only ifiaz ibz iaz ibzTherefore if liz ilz for all z C then b 0 and hence lis Clinear We set a a1 ia2 b b1 ib2 and also z x iy w u iv We may represent an
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