Algebraic Topology
《Algebraic Topology》 · 第 239 页 · Section 3.3
For a singular simplex \(\sigma:[v_0,\ldots,v_k]\to X\), the cap product is defined by \(\sigma\mathbin{\frown}\varphi=\varphi(\sigma|[v_0,\ldots,v_\ell])\,\sigma|[v_\ell,\ldots,v_k]\), giving \(C_k(X;R)\times C^\ell(X;R)\to C_{k-\ell}(X;R)\).