报告题目：Introduction to 3-/4- manifolds
报 告 人：苏乐成 Monash University；郭慧正 The George Washington University
报告时间：2025年7月7日-7月10日
报告地点：正信楼201
校内联系人：王骁 [email protected]
具体安排：
7月7日
9：30-11：30 苏乐成
Title: Hyperbolic geometry:
Content:
Poincare disk model, hyperboloid model, upper half space model; 2-d, 3-d hyperbolic geometry, geodesics, arc length, volume, isometries(Mobius transformations); ideal boundary of hyperbolic 3-space, horospheres, isometric spheres
13：30--3：30 郭慧正
Title:Introduction to Algebraic Topology in 4 Dimensions
Content:
• Properties of Algebraic Invariants
• Poincar´ e Conjecture
7月8日
9：30-11：30 苏乐成
Title: Hyperbolic knot theory:
Content:
Alternating-ness, prime-ness, geometric structure, discrete group of isometries, hyperbolic manifolds, tetrahedron, gluing and completeness equations
13：30--3：30 郭慧正
Title: Kirby Calculus
Content:
• Handles and Handle Decomposition
• Handle Moves
– Handle Slides
– Handle Cancellation
• 4-dimensional Aspects
– Dotted 1-circle Notation
– 1-handle Attachment
– Kirby Diagram
• Examples
7月9日
9：30-11：30 苏乐成
Title: Finding hyperbolic structure for knot/link complements:
Content:
Thurston's hyperbolization theorem, incompressible surfaces, checkerboard decomposition, chunk decomposition, Menasco's 1984 paper about alternating links
13：30--3：30 郭慧正
Title: Generalized Lightbulb Theorem
Content:
• 3-dimensional Version
• 4-dimensional Version (Gabai)
• Boundary Version
• Dax Invariants (Disk Version)
• Extended Relative Dax Invariant
– on S1-bundle over Σ
7月10日
9：30-11：30 苏乐成
Title: Alternating links on surfaces and wrapping up:
Content:
Diagrams on surfaces (including nonorientable), virtual/twisted links
