### Abstract

Let G be a finite group. Let f: X → Y be a k-connected, degree 1, G-framed map of simply connected, closed, oriented, smooth manifolds X and Y of dimension 2k ≧ 6. Assuming that the dimension of the singular set of the action of G on X is at most k, we construct an abelian group W(G, Y) and an element σ(f) ∈ W (G, Y), called the surgery obstruction of f, such that the vanishing of σ(f) in W (G, Y) guarantees that f can converted by G-surgery to a homotopy equivalence.

Original language | English |
---|---|

Pages (from-to) | 267-302 |

Number of pages | 36 |

Journal | Forum Mathematicum |

Volume | 8 |

Issue number | 3 |

Publication status | Published - 1996 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Forum Mathematicum*,

*8*(3), 267-302.

**Equivariant surgery with middle dimensional singular sets. I.** / Bak, Anthony; Morimoto, Masaharu.

Research output: Contribution to journal › Article

*Forum Mathematicum*, vol. 8, no. 3, pp. 267-302.

}

TY - JOUR

T1 - Equivariant surgery with middle dimensional singular sets. I

AU - Bak, Anthony

AU - Morimoto, Masaharu

PY - 1996

Y1 - 1996

N2 - Let G be a finite group. Let f: X → Y be a k-connected, degree 1, G-framed map of simply connected, closed, oriented, smooth manifolds X and Y of dimension 2k ≧ 6. Assuming that the dimension of the singular set of the action of G on X is at most k, we construct an abelian group W(G, Y) and an element σ(f) ∈ W (G, Y), called the surgery obstruction of f, such that the vanishing of σ(f) in W (G, Y) guarantees that f can converted by G-surgery to a homotopy equivalence.

AB - Let G be a finite group. Let f: X → Y be a k-connected, degree 1, G-framed map of simply connected, closed, oriented, smooth manifolds X and Y of dimension 2k ≧ 6. Assuming that the dimension of the singular set of the action of G on X is at most k, we construct an abelian group W(G, Y) and an element σ(f) ∈ W (G, Y), called the surgery obstruction of f, such that the vanishing of σ(f) in W (G, Y) guarantees that f can converted by G-surgery to a homotopy equivalence.

UR - http://www.scopus.com/inward/record.url?scp=0030304633&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030304633&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030304633

VL - 8

SP - 267

EP - 302

JO - Forum Mathematicum

JF - Forum Mathematicum

SN - 0933-7741

IS - 3

ER -