Knotted surfaces, Homological Norm and Extendable Subgroup

2025/11/05 by Liu, Qiling · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.2511.03648

openalex publication_date 2025/11/05 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/28

Abstract

We prove that for arbitrary g, there is a surface K of genus g embedded in S4, which has finitely many extendable self-homeomorphisms' action on H1(K,Z), by defining a norm on H1(K,Z) and proving its additivity.

Citations

• On dual unit balls of Thurston norms
• On slope genera of knotted tori in 4-space
• Spin structures and codimension-two homeomorphism extensions
• Extending T^p automorphisms over \RR^p+2 and realizing DE attractors

Cited by

• Exotic knottings and symmetries of surfaces in 4-manifolds

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