Communications in Analysis and Geometry

Volume 25 (2017)

Number 2

Stable cohomotopy Seiberg–Witten invariants of connected sums of four-manifolds with positive first Betti number II: Applications

Pages: 373 – 393

DOI: http://dx.doi.org/10.4310/CAG.2017.v25.n2.a4

Authors

Masashi Ishida (Mathematical Institute, Tohoku University, Sendai, Japan)

Hirofumi Sasahira (Faculty of Mathematics, Kyushu University, Nishi-ku, Fukuoka, Japan)

Abstract

This is a sequel to our article [“Stable cohomotopy Seiberg-Witten invariants of connected sums of four-manifolds with positive first Betti number, I: non-vanishing theorem”, Internat. J. Math. 26 (2015), no. 5] where a generalization of a nonvanishing theorem for stable cohomotopy Seiber–Witten invariants is proved. The main purpose of the current article is to give various applications of the non-vanishing theorem to the differential geometry and topology of 4-manifolds, including existence of exotic smooth structures, smooth connected sum decompositions of 4-manifolds and computations of Perelman’s $\bar{\lambda}$ invariant.

Full Text (PDF format)

Paper received on 11 June 2012.