arXiv subjects

Lecheng Su

Publications and source records attributed to Lecheng Su.

3 recordsLinked to original sources

arXiv2026

Octahedral decomposition of alternating links in thickened surfaces

The octahedral decomposition of classical link complements has been considered and utilised by Weeks, Rubinstein, Sakuma etc. It is even more natural to consider the octahedral decomposition of virtual link complements. In this paper, we explore and generalise the octahedral decomposition used in \emph{snappy} to links in thickened surface. Using the decomposition, we prove nonpositive curvature of the complement and essential-ness of edges in the decomposition.

math.GT↗

arXiv2024

Alternating links on nonorientable surfaces and Klein-bottly alternating links

It has been known for several decades that classical alternating links in the 3-sphere have nice hyperbolic geometric properties. Recent work generalises such results to give hyperbolic geometry of links with alternating projections onto any surface in very general 3-manifolds. However, the most general results require an orientable projection surface. In this paper, we extend to alternating links on nonorientable projection surfaces. As an application, we study Klein bottly alternating links in prism manifolds, which are a natural generalisation of Adams' toroidally alternating links in lens spaces.

math.GT↗

arXiv2024

Lambda lengths in The figure eight knot complement

In the complete hyperbolic structure on the complement of the figure eight knot, we determine the set of lambda lengths from the maximal cusp to itself. Using the correspondence between spinors and spin-decorated horospheres, we show that these lambda lengths are precisely the Eisenstein integers, up to multiplication by a unit. We also show that the inter-cusp distances from the maximal cusp to itself are precisely the norms of Eisenstein integers.

math.GT↗