Fixed Point Sets and the Fundamental Group II: Euler Characteristics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866916668602580992 |
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| author | Cappell, Sylvain Weinberger, Shmuel Yan, Min |
| author_facet | Cappell, Sylvain Weinberger, Shmuel Yan, Min |
| contents | For a group $G$ of not prime power order, Oliver showed that the obstruction for a finite CW-complex $F$ to be the fixed point set of a contractible finite $G$-CW-complex is the Euler characteristic $χ(F)$. He also has the similar results for compact Lie group actions. We show that the analogous problem for $F$ to be the fixed point set of a finite $G$-CW-complex of some given homotopy type is still determined by the Euler characteristic. Using trace maps in $K_0$, we also see that there are interesting roles for the fundamental group and the component structure of the fixed point set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_14988 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Fixed Point Sets and the Fundamental Group II: Euler Characteristics Cappell, Sylvain Weinberger, Shmuel Yan, Min Algebraic Topology 57Q91 For a group $G$ of not prime power order, Oliver showed that the obstruction for a finite CW-complex $F$ to be the fixed point set of a contractible finite $G$-CW-complex is the Euler characteristic $χ(F)$. He also has the similar results for compact Lie group actions. We show that the analogous problem for $F$ to be the fixed point set of a finite $G$-CW-complex of some given homotopy type is still determined by the Euler characteristic. Using trace maps in $K_0$, we also see that there are interesting roles for the fundamental group and the component structure of the fixed point set. |
| title | Fixed Point Sets and the Fundamental Group II: Euler Characteristics |
| topic | Algebraic Topology 57Q91 |
| url | https://arxiv.org/abs/2010.14988 |