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Link Homology in 4‐Manifolds
Author(s) -
Yasuhara Akira
Publication year - 1996
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/28.4.409
Subject(s) - mathematics , betti number , homology (biology) , manifold (fluid mechanics) , pure mathematics , intersection (aeronautics) , connection (principal bundle)
We define link homology in 4‐manifolds, and show that it has a close connection to linking numbers and intersection matrices of 4‐manifolds. We also define null‐homologous links in 4‐manifolds. We give a necessary and sufficient condition for links to be null‐homologous in 4‐manifolds. This condition implies that for any 4‐manifold with second Betti number n , there are ( n + 2)‐component links which are not nullhomologous in the 4‐manifold.