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 | References | Similar Articles | Additional Information

Abstract: We study the lagrangian embedding as a fixed point set of anti-symplectic involution on a symplectic 4-manifold . Suppose the fixed loci of are the disjoint union of smooth Riemann surfaces ; then each component becomes a lagrangian submanifold. Furthermore, if one of the components is a Riemann surface of genus , 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