Abstract
If we are given a $G$-manifold $M$, $G$ a finite abelian group of odd order, by taking fixed submanifolds $M^H$ for various subgroups $H$ of $G$, we obtain a family $(M^H)_{H \le G}$ of submanifolds of $M$. The Euler characteristics $\chi (M^H)$ of such submanifolds satisfy some congruence relations. Conversely, in this paper we show that if we are given a family $(N_i)$ of submanifolds $N_i$ of a manifold $N$ and if the Euler characteristics $\chi (N_i)$ satisfy some congruence relations, then, after adding some family, $(N_i)$ can be cut and pasted into a family obtained from a $G$-manifold.
Citation
Katsuhiro Komiya. "Cutting and pasting of manifolds into $G$-manifolds." Kodai Math. J. 26 (2) 230 - 243, June 2003. https://doi.org/10.2996/kmj/1061901064
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