تقرير
A family of Andrews-Curtis trivializations via 4-manifold trisections
| العنوان: | A family of Andrews-Curtis trivializations via 4-manifold trisections |
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| المؤلفون: | Romary, Ethan, Zupan, Alexander |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, Mathematics - Group Theory, 57K40, 57R60, 20F05 |
| الوصف: | An R-link is an $n$-component link $L$ in $S^3$ such that Dehn surgery on $L$ yields $\#^n(S^1 \times S^2)$. Every R-link $L$ gives rise to a geometrically simply-connected homotopy 4-sphere $X_L$, which in turn can be used to produce a balanced presentation of the trivial group. Adapting work of Gompf, Scharlemann, and Thompson, Meier and Zupan produced a family of R-links $L(p,q;c/d)$, where the pairs $(p,q)$ and $(c,d)$ are relatively prime and $c$ is even. For this family, $L(3,2;2n/(2n+1))$ induces the infamous trivial group presentation $\langle x,y \, | \, xyx=yxy, x^{n+1}=y^n \rangle$, a popular collection of potential counterexamples to the Andrews-Curtis conjecture for $n \geq 3$. In this paper, we use 4-manifold trisections to show that the group presentations corresponding to a different family, $L(3,2;4/d)$, are Andrews-Curtis trivial for all $d$. Comment: 12 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2304.03196 |
| رقم الأكسشن: | edsarx.2304.03196 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |