SUMMARY
The discussion centers on the citation of the statement regarding smooth k-spheres embedded in R^n, specifically that "any smooth k-sphere embedded in R^n with 2n − 3k − 3 > 0 is unknotted." The original source is identified as a 1960 paper titled "Unknotting Spheres," which is linked in the discussion. Participants note that the concept of knottedness in spheres is primarily a codimension-2 phenomenon, supported by references to Zeeman's work.
PREREQUISITES
- Understanding of knot theory and its terminology
- Familiarity with smooth manifolds and k-spheres
- Knowledge of codimension concepts in topology
- Ability to interpret mathematical papers and citations
NEXT STEPS
- Read the 1960 paper "Unknotting Spheres" for foundational knowledge
- Explore Zeeman's contributions to knot theory for deeper insights
- Study the implications of codimension in topology
- Investigate the relationship between knottedness and dimensionality in manifolds
USEFUL FOR
Mathematicians, topologists, and students studying knot theory, particularly those interested in the properties of spheres and their embeddings in higher dimensions.