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What does cap product actually mean?

By Emma Martinez
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I have read the Wikipedia definition of cap product. Here is the Wikipedia definition that I know.

What I understand: For a good space, for example, an orientable closed $n$ manifold using the Poincare Duality and definition of cup product, I can convince myself that there should be such a map, but I don't understand what this bilinear map actually mean. Can anyone please clarify the definition? I just want to know what motivates us to define cap product, and what actually it means.

Thank you very much.

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