Knot Theory
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22 Terms
Knot and Link Def
Equivalence of Knots Definition
Transverse Definition
Knot Diagram, Crossings, Under/Overcrossing Strands Definitions
Reidemeister’s Theorem and Reidemeister moves definition
Knot Invariant Definition
Orientation of Knots Definition
Connected Sum Definition
Connected Sums are Well-Defined Theorem
The connected sum DOES depend on the orientations on K1 and K2
Prime vs Composite Knots Definitions
Prime Decomposition Theorem
Open/Closed Balls, and Spheres Definitions
Open and Closed Sets Definitions
Continuous Functions Definition
Smooth Functions on Open Sets Definition
Smooth Functions on Arbitrary Subsets of Rn Definition
Homeomorphisms and Diffeomorphisms
Embedding Definition
Local Embedding Theorem
Knot Definition (Formal)
Ambient Isotopy
We can think of an ambient isotopy from K to K′as a way of smoothly deforming the ambient space to make it so that K aligns with K′
Knot Equivalence
