# A FREE ℤp-ACTION AND THE SEIBERG-WITTEN INVARIANTS

• Nakamura, Nobuhiro
• Published : 2002.01.01
• 60 6

#### Abstract

We consider the situation that ${\mathbb{Z}_p}\;=\;{\mathbb{Z}/p\mathbb{Z}}$ acts freely on a closed oriented 4-manifold X with ${b_2}^{+}\;{\geq}\;2$. In this situation, we study the relation between the Seiberg-Witten invariants of X and those of the quotient manifold $X/{\mathbb{Z}}_p$. We prove that the invariants of X are equal to those of $X/{\mathbb{Z}}_p$ modulo p.

#### Keywords

4-manifold;Seiberg-Witten invariants;group action

#### References

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#### Cited by

1. $$G$$ G -monopole invariants on some connected sums of 4-manifolds vol.178, pp.1, 2015, https://doi.org/10.1007/s10711-015-0044-1