TY - JOUR
T1 - Stable cohomotopy Seiberg-Witten invariants of connected sums of four-manifolds with positive first Betti number II
T2 - Applications
AU - Ishida, Masashi
AU - Sasahira, Hirofumi
N1 - Funding Information:
We would like to express deep gratitude to Mikio Furuta for his encouragement. Furthermore, the first author would like to express deep gratitude to Claude LeBrun for his encouragement and interest in this work. It is also pleasure for us to thank the referee for careful reading of the manuscript and useful comments. The first author is partially supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No. 20540090.
PY - 2017
Y1 - 2017
N2 - This is a sequel to our article [16] where a generalization of a non-vanishing theorem for stable cohomotopy Seiberg-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 ?¯ invariant.
AB - This is a sequel to our article [16] where a generalization of a non-vanishing theorem for stable cohomotopy Seiberg-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 ?¯ invariant.
UR - http://www.scopus.com/inward/record.url?scp=85027408128&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85027408128&partnerID=8YFLogxK
U2 - 10.4310/CAG.2017.v25.n2.a4
DO - 10.4310/CAG.2017.v25.n2.a4
M3 - Article
AN - SCOPUS:85027408128
SN - 1019-8385
VL - 25
SP - 373
EP - 393
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
IS - 2
ER -