## Tokyo Journal of Mathematics

### Equivariant Cutting and Pasting of $G$ Manifolds

Tamio HARA

#### Abstract

Let $G$ be a finite abelian group and let $SK_{*}^{G}(pt,pt)$ be a cutting and pasting group (an SK group) based on $G$ manifolds with boundary. In this paper, we first obtain a basis for a $\mathbf{Z}$ module $\mathcal{T}_{*}^{G}$ consisting of all homomorphisms ($G$-SK invariants) $T:SK_{*}^{G}(pt,pt)\rightarrow\mathbf{Z}$. Let $SK_{*}^{G}$ be the SK group based on closed $G$ manifolds. We next study a relation between the theories $SK_{*}^{G}$ and $SK_{*}^{G}(pt,pt)$ by performing equivariant cuttings and pastings of $G$ manifolds, and characterize a class of multiplicative invariants which are related to $\chi^G$.

#### Article information

Source
Tokyo J. Math., Volume 23, Number 1 (2000), 69-85.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.tjm/1255958808

Digital Object Identifier
doi:10.3836/tjm/1255958808

Mathematical Reviews number (MathSciNet)
MR1763505

Zentralblatt MATH identifier
0959.57032

#### Citation

HARA, Tamio. Equivariant Cutting and Pasting of $G$ Manifolds. Tokyo J. Math. 23 (2000), no. 1, 69--85. doi:10.3836/tjm/1255958808. https://projecteuclid.org/euclid.tjm/1255958808