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Anti-symplectic involutions with lagrangian fixed loci and their quotients


Authors: Yong Seung Cho and Dosang Joe
Journal: Proc. Amer. Math. Soc. 130 (2002), 2797-2801
MSC (2000): Primary 57N13, 57N35, 57R57
DOI: https://doi.org/10.1090/S0002-9939-02-06391-8
Published electronically: February 4, 2002
MathSciNet review: 1900887
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Abstract: We study the lagrangian embedding as a fixed point set of anti-symplectic involution $\tau$ on a symplectic 4-manifold $X$. Suppose the fixed loci of $\tau$ are the disjoint union of smooth Riemann surfaces $X^{\tau} =\dot\cup \,{\Sigma_i}$; then each component becomes a lagrangian submanifold. Furthermore, if one of the components is a Riemann surface of genus $g\ge 2$, then its quotient has vanishing Seiberg-Witten invariants. We will discuss some examples which allow an anti-symplectic involution with lagrangian fixed loci.


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Additional Information

Yong Seung Cho
Affiliation: Department of Mathematics, Ewha Women’s University, Seoul 120-750, Korea
Email: yescho@mm.ewha.ac.kr

Dosang Joe
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Korea
Email: joe@euclid.postech.ac.kr

DOI: https://doi.org/10.1090/S0002-9939-02-06391-8
Received by editor(s): October 13, 1999
Received by editor(s) in revised form: April 18, 2001
Published electronically: February 4, 2002
Additional Notes: The first author was supported in part by KOSEF grant #1999-2-101-002-5
The second author was supported in part by KOSEF grant #2000-2-10100-002-3
This work was supported in part by BK21 project
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society

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