The special shadow-complexity of $\#_k(S^1\times S^3)$

Hironobu Naoe

The special shadow-complexity of $\#_k(S^1\times S^3)$

Geometric Topology 2023-09-19 v1

Authors: Hironobu Naoe

Abstract

The special shadow-complexity is an invariant of closed $4$ -manifolds defined by Costantino using Turaev's shadows. We show that for any positive integer $k$ , the special shadow-complexity of the connected sum of $k$ copies of $S^1\times S^3$ is exactly $k+1$ .

Keywords

special shadow-complexity closed 4-manifolds connected sum turaev shadows invariant

Cite

@article{arxiv.2309.09225,
  title  = {The special shadow-complexity of $\#_k(S^1\times S^3)$},
  author = {Hironobu Naoe},
  journal= {arXiv preprint arXiv:2309.09225},
  year   = {2023}
}

Comments

12 pages, 6 figures

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