Matches in SemOpenAlex for { <https://semopenalex.org/work/W4323927092> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W4323927092 abstract "We develop a new algebraic theory of positive braids and conjugacy classes in the braid group $B_3$. We use our theory to establish a complete classification of isotopy classes of degree three symplectic curves in $mathbb{CP}^2$ with only $A_n$-singularities for $ngeq 1$ (an $A_n$-singularity is locally modelled by the equation $z^2 = w^n$) independent of Gromov's theory of pseudoholomorphic curves. We show that if $C$ and $C'$ are degree three symplectic curves in $mathbb{CP}^2$ with the same numbers of $A_n$-singularities for each $ngeq 1$, then $C$ is isotopic to $C'$. Furthermore, our theory furnishes a single method of proof that independently establishes and unifies several fundamental classification results on degree three symplectic curves in $mathbb{CP}^2$. In particular, we prove using our theory: (1) there is a unique isotopy class of degree three smooth symplectic curves in $mathbb{CP}^2$ (a result due to Sikorav), (2) the number of nodes is a complete invariant of the isotopy class of a degree three nodal symplectic curve in $mathbb{CP}^2$ (the case of irreducible nodal curves is due to Shevchishin and the case of reducible nodal curves is due to Golla-Starkston), and (3) there is a unique isotopy class of degree three cuspidal symplectic curves in $mathbb{CP}^2$ (a generalization of a result due to Ohta-Ono). The present work represents the first step toward resolving the symplectic isotopy conjecture using purely algebraic techniques in the theory of braid groups. Finally, we independently establish a complete classification of genus one Lefschetz fibrations over $mathbb{S}^2$ (a result due to Moishezon-Livne)." @default.
- W4323927092 created "2023-03-12" @default.
- W4323927092 creator A5089804521 @default.
- W4323927092 date "2023-03-09" @default.
- W4323927092 modified "2023-09-30" @default.
- W4323927092 title "The complete classification of isotopy classes of degree three symplectic curves in $mathbb{CP}^2$ via a novel algebraic theory of braid monodromy" @default.
- W4323927092 doi "https://doi.org/10.48550/arxiv.2303.05281" @default.
- W4323927092 hasPublicationYear "2023" @default.
- W4323927092 type Work @default.
- W4323927092 citedByCount "0" @default.
- W4323927092 crossrefType "posted-content" @default.
- W4323927092 hasAuthorship W4323927092A5089804521 @default.
- W4323927092 hasBestOaLocation W43239270921 @default.
- W4323927092 hasConcept C114614502 @default.
- W4323927092 hasConcept C121332964 @default.
- W4323927092 hasConcept C124194741 @default.
- W4323927092 hasConcept C12843 @default.
- W4323927092 hasConcept C134306372 @default.
- W4323927092 hasConcept C159985019 @default.
- W4323927092 hasConcept C168619227 @default.
- W4323927092 hasConcept C192562407 @default.
- W4323927092 hasConcept C202444582 @default.
- W4323927092 hasConcept C207043602 @default.
- W4323927092 hasConcept C24890656 @default.
- W4323927092 hasConcept C2775997480 @default.
- W4323927092 hasConcept C2778876713 @default.
- W4323927092 hasConcept C33840335 @default.
- W4323927092 hasConcept C33923547 @default.
- W4323927092 hasConcept C68363185 @default.
- W4323927092 hasConcept C87945829 @default.
- W4323927092 hasConcept C96403706 @default.
- W4323927092 hasConceptScore W4323927092C114614502 @default.
- W4323927092 hasConceptScore W4323927092C121332964 @default.
- W4323927092 hasConceptScore W4323927092C124194741 @default.
- W4323927092 hasConceptScore W4323927092C12843 @default.
- W4323927092 hasConceptScore W4323927092C134306372 @default.
- W4323927092 hasConceptScore W4323927092C159985019 @default.
- W4323927092 hasConceptScore W4323927092C168619227 @default.
- W4323927092 hasConceptScore W4323927092C192562407 @default.
- W4323927092 hasConceptScore W4323927092C202444582 @default.
- W4323927092 hasConceptScore W4323927092C207043602 @default.
- W4323927092 hasConceptScore W4323927092C24890656 @default.
- W4323927092 hasConceptScore W4323927092C2775997480 @default.
- W4323927092 hasConceptScore W4323927092C2778876713 @default.
- W4323927092 hasConceptScore W4323927092C33840335 @default.
- W4323927092 hasConceptScore W4323927092C33923547 @default.
- W4323927092 hasConceptScore W4323927092C68363185 @default.
- W4323927092 hasConceptScore W4323927092C87945829 @default.
- W4323927092 hasConceptScore W4323927092C96403706 @default.
- W4323927092 hasLocation W43239270921 @default.
- W4323927092 hasOpenAccess W4323927092 @default.
- W4323927092 hasPrimaryLocation W43239270921 @default.
- W4323927092 hasRelatedWork W1530524032 @default.
- W4323927092 hasRelatedWork W1806022941 @default.
- W4323927092 hasRelatedWork W187468811 @default.
- W4323927092 hasRelatedWork W2053636290 @default.
- W4323927092 hasRelatedWork W2083660270 @default.
- W4323927092 hasRelatedWork W2949957802 @default.
- W4323927092 hasRelatedWork W2963673189 @default.
- W4323927092 hasRelatedWork W3099103747 @default.
- W4323927092 hasRelatedWork W566125649 @default.
- W4323927092 hasRelatedWork W620929764 @default.
- W4323927092 isParatext "false" @default.
- W4323927092 isRetracted "false" @default.
- W4323927092 workType "article" @default.