• Corpus ID: 231592898

Instanton Floer homology, sutures, and Euler characteristics

@inproceedings{Li2021InstantonFH,
  title={Instanton Floer homology, sutures, and Euler characteristics},
  author={Zhenkun Li and Fan Ye},
  year={2021}
}

• Zhenkun Li, Fan Ye
• Published 13 January 2021
• Mathematics

This is a companion paper to an earlier work of the authors. In this paper, we provide an axiomatic definition of Floer homology for balanced sutured manifolds and prove that the graded Euler characteristic χgr of this homology is fully determined by the axioms we proposed. As a result, we conclude that χgrpSHIpM,γqq “ χgrpSFHpM,γqq for any balanced sutured manifold pM,γq. In particular, for any link L in S3, the Euler characteristic χgrpKHIpS, Lqq recovers the multi-variable Alexander polynomial of L, which generalizes the knot case. Combined with the authors’ earlier work, we provide more examples of p1, 1q-knots in lens spaces whose KHI and { HFK have the same dimension. Moreover, for a rationally null-homologous knot in a closed oriented 3-manifold Y , we construct canonical Z2-gradings on KHIpY,Kq, the decomposition of I7pY q discussed in the previous paper, and the minus version of instanton knot homology KHI ́pY,Kq introduced by the first author.