RASMUSSEN INVARIANT, SLICE-BENNEQUIN INEQUALITY, AND SLICENESS OF KNOTS

Autor:	Alexander N. Shumakovitch
Rok vydání:	2007
Předmět:	Mathematics - Geometric Topology Pure mathematics Algebra and Number Theory 57M25 57M27 FOS: Mathematics Combinatorial proof Geometric Topology (math.GT) Invariant (mathematics) Mathematics::Symplectic Geometry Mathematics::Geometric Topology Slice genus Mathematics
Zdroj:	Journal of Knot Theory and Its Ramifications. 16:1403-1412
ISSN:	1793-6527 0218-2165
DOI:	10.1142/s0218216507005889
Popis:	We use recently introduced Rasmussen invariant to find knots that are topologically locally-flatly slice but not smoothly slice. We note that this invariant can be used to give a combinatorial proof of the slice-Bennequin inequality. Finally, we compute the Rasmussen invariant for quasipositive knots and show that most of our examples of non-slice knots are not quasipositive and, to the best of our knowledge, were previously unknown. 9 pages, 4 tables and 1 figure. Updated to match the published version: Corollary 1.D is made more general to work with links instead of knots, a comment on the relation between the total rank of the reduced Khovanov homology and computations of the Rasmussen invariant is added. Journal reference is added and references are updated
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::117a08783ed1b0a1529d7100faeda1da https://doi.org/10.1142/s0218216507005889 Zobrazit plný text záznamu