Equivariant Cutting and Pasting of $G$ Manifolds

HARA, Tamio

HARA, Tamio

Tokyo J. of Math., Tome 23 (2000) no. 2, p. 69-85 / Harvested from Project Euclid

Résumé

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 $\chi^G$.

Publié le : 2000-06-15
Classification:

@article{1255958808,
     author = {HARA, Tamio},
     title = {Equivariant Cutting and Pasting of $G$ Manifolds},
     journal = {Tokyo J. of Math.},
     volume = {23},
     number = {2},
     year = {2000},
     pages = { 69-85},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255958808}
}

HARA, Tamio. Equivariant Cutting and Pasting of $G$ Manifolds. Tokyo J. of Math., Tome 23 (2000) no. 2, pp.  69-85. http://gdmltest.u-ga.fr/item/1255958808/