The geography problem for 4-manifolds with specified fundamental group
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- by Paul Kirk and Charles Livingston PDF
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Abstract:
For any class $\mathcal {M}$ of 4–manifolds, for instance the class $\mathcal {M}(G)$ of closed oriented manifolds with $\pi _1(M) \cong G$ for a fixed group $G$, the geography of $\mathcal {M}$ is the set of integer pairs $\{(\sigma (M), \chi (M)) | M \in \mathcal {M}\}$, where $\sigma$ and $\chi$ denote the signature and Euler characteristic. This paper explores general properties of the geography of $\mathcal {M}(G)$ and undertakes an extended study of $\mathcal {M}(\mathbf {Z}^n)$.References
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Additional Information
- Paul Kirk
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 266369
- Email: pkirk@indiana.edu
- Charles Livingston
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 193092
- Email: livingst@indiana.edu
- Received by editor(s): May 25, 2007
- Published electronically: March 16, 2009
- Additional Notes: This work was supported by grants from the NSF
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 361 (2009), 4091-4124
- MSC (2000): Primary 57M05, 57N13, 57R19
- DOI: https://doi.org/10.1090/S0002-9947-09-04649-2
- MathSciNet review: 2500880