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Number of Minimal Components and Homologically Independent  Form

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okay welcome everyone to my continuation of what is algebraic topology today probably the main player of algebraic topology homology more precisely simplicial and singular homology uh turns out that they are the same at least for reasonable spaces so singular homology is a general definition simplicial homology is a computable definition and as i said for all reasonable spaces they turn out to be the same and the idea is this idea of cycles modular boundaries and we will see well throughout this talk so i will mostly explain what simplicial homology is because it's just easy and computable and really combinatorial um but that as a at the end you will also see singular homology and as i said the main point is that they are kind of the same anyway up to some very general topological spaces where you just can't apply similar as simplicial homology so the pleasure homology in some sense is really nice because it's breakfast for a computer it might be hard to get your head around it if you

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