A note on grid homology in lens spaces: \(\mathbb{Z}\) coefficients and computations. (English) Zbl 1522.57009
Summary: We present a combinatorial proof for the existence of the sign-refined grid homology in lens spaces and a self-contained proof that \(\partial_{\mathbb{Z}}^2 = 0\). We also present a Sage programme that computes \(\widehat{\mathrm{GH}} (L(p, q), K; \mathbb{Z})\) and provide empirical evidence supporting the absence of torsion in these groups.
Editorial remark: The original proof that \(\partial_{\mathbb{Z}}^2 = 0\) in [K. L. Baker et al., Int. Math. Res. Not. 2008, Article ID rnn024, 39 p. (2008; Zbl 1168.57009)] was indirect and relied on the well-definedness of the analytic theory.
Editorial remark: The original proof that \(\partial_{\mathbb{Z}}^2 = 0\) in [K. L. Baker et al., Int. Math. Res. Not. 2008, Article ID rnn024, 39 p. (2008; Zbl 1168.57009)] was indirect and relied on the well-definedness of the analytic theory.
Citations:
Zbl 1168.57009References:
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