Reidemeister and movie moves for involutive links
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913151794020352 |
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| author | Borodzik, Maciej Dai, Irving Mallick, Abhishek Stoffregen, Matthew |
| author_facet | Borodzik, Maciej Dai, Irving Mallick, Abhishek Stoffregen, Matthew |
| contents | An involutive link is a link which is invariant under the standard rotation by 180 degrees in $S^3$. We establish an equivariant analogue of the work of Carter and Saito aimed at studying equivariant cobordisms between involutive links. This gives a set of $39$ equivariant movie moves that suffice to go between any two movie presentations of a pair of equivariantly isotopic cobordisms. Along the way, we give a singularity-theoretic proof of the equivariant Reidemeister theorem and study loops of equivariant Reidemeister moves. Our approach proceeds by analyzing codimension $2$ singularities of equivariant maps from $S^1$ to $\mathbb{R}^2$, as well as utilizing embedded equivariant Morse theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_26369 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reidemeister and movie moves for involutive links Borodzik, Maciej Dai, Irving Mallick, Abhishek Stoffregen, Matthew Geometric Topology An involutive link is a link which is invariant under the standard rotation by 180 degrees in $S^3$. We establish an equivariant analogue of the work of Carter and Saito aimed at studying equivariant cobordisms between involutive links. This gives a set of $39$ equivariant movie moves that suffice to go between any two movie presentations of a pair of equivariantly isotopic cobordisms. Along the way, we give a singularity-theoretic proof of the equivariant Reidemeister theorem and study loops of equivariant Reidemeister moves. Our approach proceeds by analyzing codimension $2$ singularities of equivariant maps from $S^1$ to $\mathbb{R}^2$, as well as utilizing embedded equivariant Morse theory. |
| title | Reidemeister and movie moves for involutive links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2604.26369 |