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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Bordism of spin 4-manifolds
with local action of tori


Author: Piotr Mikrut
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
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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 Wrocław, pl.Grunwaldzki 2/4, 50-384 Wrocław, Poland
Email: mikrut@math.uni.wroc.pl

DOI: https://doi.org/10.1090/S0002-9947-98-02355-1
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
Article copyright: © Copyright 1998 American Mathematical Society