Chromatic Homotopy Theory
《Chromatic Homotopy Theory》 · 第 316–317 页 · Section 10.3.1，构造数据与 Definition 10.3.1（有向三维流形约定）
Let \(M\) be the (unique) oriented bundle \(S\mathbin{\overset{(\sim)}{\times}}S^1\) over a compact connected (possibly non-orientable) surface \(S\) with boundary. We denote by \(S\) the zero-section. Let \(T_1,\ldots,T_k\) be the boundary tori of \(M\). On each \(T_i\) we choose an orientation for the meridian \(m_i=T_i\cap\partial S\) and for the fibre \(l_i\) of the bundle so that the basis \((m_i,l_i)\) for \(H_1(T_i,\mathbb Z)\) be positively oriented. A \((p_i,q_i)\)-Dehn filling on \(T_i\) kills the slope \(p_im_i+q_il_i\). We say that the Dehn filling is fibre-parallel if \(p_i=0\), i.e. if it kills a fibre. A Seifert manifold is any 3-manifold \(N\) obtained from \(M\) by Dehn filling some \(h\le k\) boundary tori in a non-fibre-parallel way, that is with \(p_i\ne0\) for all \(i\).