Open Access
June 2017 Equivariant Bauer-Furuta invariants on Some Connected Sums of 4-manifolds
Chanyoung SUNG
Tokyo J. Math. 40(1): 53-63 (June 2017). DOI: 10.3836/tjm/1502179215


On some connected sums of 4-manifolds with natural actions of finite groups, we use equivariant Bauer-Furuta invariant to deduce the existence of solutions of Seiberg-Witten equations invariant under the group actions. For example, for any integer $k\geq 2$ we show that the connected sum of $k$ copies of a 4-manifold $M$ with nontrivial Bauer-Furuta invariant has a nontrivial $\mathbb{Z}_k$-equivariant Bauer-Furuta invariant for the obviously glued Spin$^c$ structure, where the $\mathbb{Z}_k$-action cyclically permutes $k$ summands of $M$. This contrasts with the fact that ordinary Bauer-Furuta invariants of such connected sums are all trivial for any sufficiently large $k$, when $b_1(M)=0$.


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Chanyoung SUNG. "Equivariant Bauer-Furuta invariants on Some Connected Sums of 4-manifolds." Tokyo J. Math. 40 (1) 53 - 63, June 2017.


Published: June 2017
First available in Project Euclid: 8 August 2017

zbMATH: 06787087
MathSciNet: MR3689978
Digital Object Identifier: 10.3836/tjm/1502179215

Primary: 57R57
Secondary: 57M60

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

Vol.40 • No. 1 • June 2017
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