Suppose c is a k+1 chain in U(open set in space R^n), then boundary of c (a k chain) can be expressed as a linear combination of k-cubes, using boundary operator: $$∂c=∑_ia_ic_i$$, where a_i are the coefs. Above is my understanding so far about relations brought by boundary operator, and now I am asked to show that sum of these coefs is 0, namely: $$∑_ia_i=0$$, I don't even see why this is even true. How should I approach this? Thanks for any suggestions.
2025-01-13 02:39:11.1736735951
property of sum of coefs of a chain
36 Views Asked by jfcjohn https://math.techqa.club/user/jfcjohn/detail AtRelated Questions in DIFFERENTIAL-GEOMETRY
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