Abstract:
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. In this talk, 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. Furthermore, we will discuss the joint work with T. Fiedler on the quantum equations derived from a regular 1-cocycle based on the HOMFLY-PT polynomial.
Language: English
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
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