2022/12/27 by Duncan McCoy, Clayton McDonald
Mathematics · #Algebraic structures and combinatorial models #Artificial intelligence #Bijection #Bijection, injection and surjection #Biology #Combinatorics #Computer science #Embedding #Fibered knot #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Slicing
paper · pdf · doi:10.1307/mmj/20216077
openalex publication_date 2022/12/27 · crossref created 2022/12/27 · crossref issued 2024/02/01 · crossref published 2024/02/01 · crossref published-print 2024/02/01 · crossref deposited 2024/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11 · crossref indexed 2026/07/26
In this paper, we compare the notions of double sliceness for links. The main result is showing that a large family of 2-component Montesinos links are not strongly doubly slice despite being weakly doubly slice and having doubly slice components. Our principal obstruction to strong double slicing comes by considering branched double covers. To this end, we prove a result classifying Seifert fibered spaces that admit a smooth embedding into integer homology S1×S3s by maps inducing surjections on the first homology group. A number of other results and examples pertaining to doubly slice links are also given.