### Abstract

Let G be a finite group and let f : X → Y be a degree 1, G-framed map such that X and Y are simply connected, closed, oriented, smooth manifolds of dimension n = 2k ≧ 6 and such that the dimension of the singular set of the G-space X is at most k. In the previous article, assuming f is k-connected, we defined the G-equivariant surgery obstruction σ(f) in a certain abelian group. There it was shown that if σ(f) = 0 then f is G-framed cobordant to a homotopy equivalence f′ : X′ → Y. In the present article, we prove that the obstruction σ(f) is a G-framed cobordism invariant. Consequently, the G-surgery obstruction σ(f) is uniquely associated to f : X σ Y above even if it is not k-connected.

Original language | English |
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Pages (from-to) | 2427-2440 |

Number of pages | 14 |

Journal | Transactions of the American Mathematical Society |

Volume | 353 |

Issue number | 6 |

Publication status | Published - Dec 1 2001 |

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### Keywords

- Cobordism invariant
- Equivariant surgery
- Quadratic module
- Surgery obstruction

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics