Seiberg-Witten invariants of non-simple type and Einstein metrics

2000/02/28 by Heberto del Rio Guerra, Guerra, Heberto del Rio
Mathematics · #53C25 #53C27 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C25 #msc:53C27

paper · pdf · doi:10.48550/arxiv.math/0002243

19 pages, LaTeX

arxiv created 2000/02/28 · arxiv updated 2009/11/30

Abstract

We construct examples of four dimensional manifolds with Spin^c-structures, whose moduli spaces of solutions to the Seiberg-Witten equations, represent a non-trivial bordism class of positive dimension, i.e. the Spin^c-structures are not induced by almost complex structures. As an application, we show the existence of infinitely many non-homeomorphic compact oriented 4-manifolds with free fundamental group and predetermined Euler characteristic and signature that do not carry Einstein metrics.

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