PreprintCC BY 4.0arXiv
Reducible handle additions along separating slopes
Abstract
Let M be a compact orientable simple 3-manifold, and let F be a component of the boundary of M with genus at least two. Suppose that alpha and beta are separating slopes on F and that both M(alpha) and M(beta) are reducible. We prove that the distance between alpha and beta is zero. Thus the reducible-reducible case of the conjecture of Qiu and Zhang on separating degenerating slopes holds in arbitrary boundary genus.
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BibTeX
@misc{guo2026reducible,
title = {{Reducible handle additions along separating slopes}},
author = {Qilong Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08145},
eprint = {2610.08145},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08145},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reducible handle additions along separating slopes
AU - Qilong Guo
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08145
UR - https://arxiv.org/abs/2610.08145
AB - Let M be a compact orientable simple 3-manifold, and let F be a component of the boundary of M with genus at least two. Suppose that alpha and beta are separating slopes on F and that both M(alpha) and M(beta) are reducible. We prove that the distance between alpha and beta is zero. Thus the reducible-reducible case of the conjecture of Qiu and Zhang on separating degenerating slopes holds in arbitrary boundary genus.
ER -