Definition 10.2.22 (Unoriented bordism spectrum). We define the unoriented bordism spectrum \(\MO \) as the Thom spectrum of the restriction of \(J\) to the virtual-rank-zero component: \[ \MO \quad := \quad \th (J\vert _{\bB O}) \quad = \quad \colim \big (J\colon \bB O\to \Sp \big ). \]
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