Bordism of spin 4-manifolds with local action of tori
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Abstract:
We prove that bordism group of spin $4$-manifolds with singular $T$-structure, the notion introduced by Cheeger and Gromov, is an infinite cyclic group and is detected by singnature. In particular we obtain that the theorem of Atiyah and Hirzebruch of vanishing of Â-genus in case of $S^{1}$ action on spin $4n$-manifolds is not valid in case of $T$-structures on spin $4$-manifolds.References
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Additional Information
- Piotr Mikrut
- Affiliation: Mathematical Institute, University of Wrocław, pl.Grunwaldzki 2/4, 50-384 Wrocław, Poland
- Email: mikrut@math.uni.wroc.pl
- Received by editor(s): June 25, 1996
- Additional Notes: The author was partially supported by the Polish Commitee of Scientific Research grant 4241/PB/IM/95
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 4423-4444
- MSC (1991): Primary 57M60, 57N13, 57R15, 57R20, 57R85
- DOI: https://doi.org/10.1090/S0002-9947-98-02355-1
- MathSciNet review: 1615930