Combinatorial 1-Cocycles of String Links Using Gauss Diagrams

par Butian Zhang

vendredi 19 déc. 2025, 16:00 → 19:30 Europe/Paris

Amphithéâtre Laurent Schwartz, bâtiment 1R3 (Institut de Mathématiques de Toulouse)

Amongst other things we are interested in combinatorial 1-cocycles of order 4 in the space of long knots. 
The space of long knots (i.e., the smooth embeddings of ℝ into ℝ³ that agree with the standard embedding of the x-axis outside the interval [-1, 1]) has been studied from various perspectives. We adopt a combinatorial approach to loops and 1-cocycles in this space. Using Gauss diagrams, we construct two nontrivial linearly independent combinatorial 1-cocycles of order 4 over ℤ and an additional one over ℤ/2ℤ. We also calculate their values on several arcs and loops in the space of long knots, yielding finite type invariants.