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Reducible smooth structures on 4‐manifolds with zero signature
Author(s) -
Akhmedov Anar,
Ishida Masashi,
Park B. Doug
Publication year - 2014
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/jtopol/jtt043
Subject(s) - mathematics , signature (topology) , zero (linguistics) , diffeomorphism , integer (computer science) , construct (python library) , pure mathematics , topology (electrical circuits) , combinatorics , geometry , computer science , philosophy , linguistics , programming language
For every large enough integer k that is not divisible by 4, we construct infinite families of mutually non‐diffeomorphic reducible smooth structures on the topological 4‐manifolds 2 k ( S 2 × S 2 ) and 2 k ( ℂ ℙ 2 #ℂ ℙ ¯ 2 ) , the connected sums of 2 k copies of S 2 × S 2 and ℂ ℙ 2 #ℂ ℙ ¯ 2 .