On the weak reducing pairs in critical Heegaard splitting
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909416298643456 |
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| author | Sun, Dongqi E, Qiang |
| author_facet | Sun, Dongqi E, Qiang |
| contents | A weak reducing pair in a Heegaard splitting M = V \cup_S W is a pair of disjoint essential disks D \in V and E \in W. The weakly reducible Heegaard splitting contains at least one weak reducing pair. Critical Heegaard splitting is a special case of weakly reducible Heegaard splitting which contains at least two weak reducing pairs satisfying some special conditions. In this paper, we discuss the properties of weak reducing pairs in a critical Heegaard splitting and give a necessary condition for Heegaard surface to be critical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the weak reducing pairs in critical Heegaard splitting Sun, Dongqi E, Qiang Geometric Topology 57K20, 57M50 A weak reducing pair in a Heegaard splitting M = V \cup_S W is a pair of disjoint essential disks D \in V and E \in W. The weakly reducible Heegaard splitting contains at least one weak reducing pair. Critical Heegaard splitting is a special case of weakly reducible Heegaard splitting which contains at least two weak reducing pairs satisfying some special conditions. In this paper, we discuss the properties of weak reducing pairs in a critical Heegaard splitting and give a necessary condition for Heegaard surface to be critical. |
| title | On the weak reducing pairs in critical Heegaard splitting |
| topic | Geometric Topology 57K20, 57M50 |
| url | https://arxiv.org/abs/2404.18382 |