Branched covers along real parts

Author:
Shuguang Wang

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2803-2808

MSC (1991):
Primary 57R55, 57R57, 57N13; Secondary 14P25

DOI:
https://doi.org/10.1090/S0002-9939-97-03935-X

MathSciNet review:
1401756

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the double cover of a Kähler surface branched along the fixed point set of an anti-holomorphic involution admits a symplectic structure.

**1.**S. Akbulut,*On quotients of complex surfaces under complex conjugation*, J. Reine Angew. Math.**447**(1994), 83-90. MR**95c:57030****2.**V. Arnold,*On the location of ovals of real algebraic plane curves, involutions on 4-dimensional smooth manifolds, and the arithmetic of integral quadratic forms*, Funct. Analy. Appl.**5**(1971), 1-9. MR**44:3999****3.**W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces, Springer-Verlag Berlin Heidelberg, 1984. MR**86c:32026****4.**S. Donaldson,*Yang-Mills invariants of four-manifolds*, In Geometry of low-dimensional manifolds. Vol 1, pp 5-41. S.K. Donaldson and C.B. Thomas Eds., Cambridge University Press, 1990. MR**93f:57040****5.**A. Edmonds,*Orientability of fixed point sets*, Proc. Amer. Math. Soc.**82**(1981), 120-125. MR**82h:57032****6.**R. Gompf,*A new construction of symplectic manifolds*, Ann. Math.**142**(1995), 527-595. MR**96g:57025****7.**S. Finashin,*Decomposability of quotients by complex conjugation for complete intersection surfaces*, Revista Mat. Univ. Comp. Madrid (to appear).**8.**R. Friedman and J. Morgan,*Algebraic surfaces and Seiberg-Witten invariants*, Preprint (1995).**9.**D. Kotschick,*On irreducible four-manifolds*, Preprint (1995).**10.**P. Kronheimer and T. Mrowka,*The genus of embedded surfaces in the projective plane*, Math. Res. Letters**1**(1994), 797-808. MR**96a:57073****11.**D. McDuff,*Examples of simply-connected symplectic non-Kählerian manifolds*, J. Diff. Geom.**20**(1984), 267-277. MR**86c:57036****12.**J. Morgan, Z. Szabo and C. Taubes,*A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture*, Preprint (1995).**13.**Y. Ruan,*Virtual neighborhoods and monopole equations*, Preprint (1996).**14.**C. Taubes,*The Seiberg-Witten invariants and symplectic forms*, Math. Research Letters**1**(1994), 809-822. MR**95j:57039****15.**W. Thurston,*Some simple examples of symplectic manifolds*, Proc. Amer. Math. Soc.**55**(1976), 467-469. MR**53:6578****16.**O. Viro,*Construction of M-surfaces*, Funct. Analy. Appl.**13**(1979), 212-213. MR**80j:14034****17.**-,*Complex orientations of real algebraic surfaces*, Topology of manifolds and varieties, Ed. O. Viro. Advances in Soviet Mathematics, Vol 18. Published by American Mathematical Society. (1994), 261-284. MR**96f:14068****18.**S. Wang,*A vanishing theorem for Seiberg-Witten invariants*, Math. Res. Letters**2**(1995), 305-310.**19.**G. Wilson,*On Hilbert sixteenth problem*, Topology**17**(1978), 53-73. MR**58:16684**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
57R55,
57R57,
57N13,
14P25

Retrieve articles in all journals with MSC (1991): 57R55, 57R57, 57N13, 14P25

Additional Information

**Shuguang Wang**

Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211

Email:
sw@wang.math.missouri.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03935-X

Keywords:
Branched cover,
real part,
symplectic structure

Received by editor(s):
March 22, 1996

Received by editor(s) in revised form:
April 30, 1996

Communicated by:
Ronald A. Fintushel

Article copyright:
© Copyright 1997
American Mathematical Society