Bordism of spin 4-manifolds with local action of tori

Mikrut, Piotr

doi:10.1090/S0002-9947-98-02355-1

Bordism of spin 4-manifolds with local action of tori
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Trans. Amer. Math. Soc. 350 (1998), 4423-4444 Request permission

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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