Furuta, M. Monopole equation and the \(\frac{11}{8}\)-conjecture. (English) Zbl 0984.57011 Math. Res. Lett. 8, No. 3, 279-291 (2001). If \(M\) is a smooth oriented closed spin 4-dimensional manifold, a well-known open conjecture is that \(M\) satisfies \(b_2(M)\geq {{11}\over{8}} |\sigma(M)|\), where \(b_2(M)\) and \(\sigma(M)\) are the second Betti number and signature of \(M\), respectively. (This is known as the 11/8 conjecture.) In this paper, the author proves the weaker inequality \(b_2(M)\geq {{5}\over{4}} |\sigma(M)|+2\). This result, first announced in 1995, is proven using Seiberg-Witten theory. A central idea in the proof is to make use of a finite-dimensional approximation to the usual Seiberg-Witten equations. The author analyzes the \(\text{Pin}_2\) symmetry of these equations, and uses equivariant K-theory to derive the above inequality. Reviewer: Terry Fuller (Northridge) Cited in 11 ReviewsCited in 53 Documents MSC: 57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) 57R57 Applications of global analysis to structures on manifolds Keywords:Seiberg-Witten theory; 4-manifold Citations:Zbl 0983.57022 PDFBibTeX XMLCite \textit{M. Furuta}, Math. Res. Lett. 8, No. 3, 279--291 (2001; Zbl 0984.57011) Full Text: DOI