Quandle Cohomology and State-sum Invariants of Knotted Curves and Surfaces (1999)
Carter, J. Scott, Jelsovsky, Daniel, Kamada, Seiichi, Langford, Laurel, Saito, Masahico
The 2-twist spun trefoil is an example of a sphere that is knotted in 4-dimensional space. Here this example is shown to be distinct from the same sphere with the reversed orientation. To demonstrate...
State-sum Invariants of Knotted Curves and Surfaces from Quandle Cohomology (1999)
J. Scott Carter, Daniel Jelsovsky, Seiichi Kamada, Laurel Langford, Masahico Saito
State-sum invariants for classical knots and knotted surfaces in 4space are developed via the cohomology theory of quandles. Cohomology of quandles are computed to evaluate the invariants. Some twist...
Quandle Cohomology and State-sum Invariants of Knotted Curves and Surfaces (1999)
J. Scott Carter, Daniel Jelsovsky, Seiichi Kamada, Laurel Langford, Masahico Saito
The 2-twist spun trefoil is an example of a sphere that is knotted in 4-dimensional space. Here this example is shown to be distinct from the same sphere with the reversed orientation. To demonstrate...
Higher-Dimensional Algebra IV: 2-Tangles (1998)
Baez, John C., Langford, Laurel
Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R^4 can be described as certain...
Baez, John C., Langford, Laurel
Just as links may be algebraically described as certain morphisms in the category of tangles, compact surfaces smoothly embedded in R^4 may be described as certain 2-morphisms in the 2-category of...
Just as links may be algebraically described as certain morphisms in the category of tangles, compact surfaces smoothly embedded in R 4 may be described as certain 2-morphisms in the 2-category of...
Higher-Dimensional Algebra IV: 2-Tangles
Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R 4 can be described as certain...