2021/07/23 by Maria Marchwicka, Marchwicka, Maria, Wojciech Politarczyk +1
Computer Science · Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2107.11299
openalex publication_date 2021/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give examples of a linear combination of algebraic knots and their mirrors that are algebraically slice, but whose topological and smooth four-genus is two. Our examples generalize an example of non-slice algebraically slice linear combination of iterated torus knots obtained by Hedden, Kirk and Livingston. Our main tool is a genus bound from Casson--Gordon invariants and a cabling formula that allows us to compute effectively these invariants.