3차원 접촉 다양체에 대한 양적 긴밀성: 부리만 기하학적 접근
본 논문에서는 부리만 기하학적 도구, 특히 접촉 야코비 곡선을 사용하여 3차원 접촉 다양체에서 리브 궤도 주변의 최대 긴밀 근방에 대한 양적 추정을 제시합니다.
Quantitative Tightness of Three-Dimensional Contact Manifolds: A Sub-Riemannian Geometry Approach
This research paper leverages sub-Riemannian geometry to establish quantitative estimates for the maximal tight neighborhood of Reeb orbits in three-dimensional contact manifolds, introducing the concept of contact Jacobi curves to detect overtwisted disks and providing sharp tightness radius estimates based on Schwarzian derivative and canonical curvature bounds.
A Topological Characterization of Contractible Bypass Embeddings in Contact 3-Manifolds
A family of bypass embeddings with a fixed attaching arc in a contact 3-manifold is contractible if there exists a "bypass in the middle" disjoint from the family away from the attaching region. This implies that interesting bypass embeddings, in terms of contact isotopy, must intersect.
從 +1 手術構造代數過扭緊 3-流形
本文探討了通過接觸 +1 手術構造代數過扭但仍然緊緻的 3-流形的現象，特別關注於沿著具有最大 Thurston–Bennequin 不變量的 Legendrian 正環面紐結和某些正辮的 Legendrian 彩虹閉包進行手術的情況。
Algebraically Overtwisted but Still Tight 3-Manifolds Constructed via Contact +1 Surgeries
This research paper presents a method for constructing examples of 3-manifolds that are algebraically overtwisted, meaning their contact homology vanishes, yet remain tight, challenging the straightforward connection between these properties.
On the Possibility of a Contact Analogue of the Kirby Move of Type 1 for Contact Surgery Diagrams
While a contact analogue of the Kirby move of type 2 exists for contact surgery diagrams, the existence of a type 1 analogue remains an open question, with this paper outlining the necessary conditions for such a move and exploring potential candidates.
두 개의 홉프 링크의 강 예외적 르장드리안 연결 합
본 논문에서는 접촉 3-구에서 두 개의 홉프 링크의 연결 합에 대한 강 예외적 르장드리안 실현의 완전한 대략적 분류를 제시합니다.
The Classification of Strongly Exceptional Legendrian Representations of the Connected Sum of Two Hopf Links in Contact 3-Spheres
This research paper presents a complete classification of strongly exceptional Legendrian realizations of the connected sum of two Hopf links in contact 3-spheres, providing a novel contribution to the understanding of exceptional Legendrian representatives for connected sums of link families.
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