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Bordism of spin 4-manifolds with local action of tori

Author(s): Piotr Mikrut
Journal: Trans. Amer. Math. Soc. 350 (1998), 4423-4444.
MSC (1991): Primary 57M60, 57N13, 57R15, 57R20, 57R85
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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.

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Additional Information:

Piotr Mikrut
Affiliation: Mathematical Institute, University of Wroclaw, pl.Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Email: mikrut@math.uni.wroc.pl

DOI: 10.1090/S0002-9947-98-02355-1
PII: S 0002-9947(98)02355-1
Keywords: $T$-structure, bordism, spin manifold, 4-manifold, signature
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 of article: Copyright 1998, American Mathematical Society

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