Topologically slice knots with nontrivial Alexander polynomial
Abstract
Let CT be the subgroup of the smooth knot concordance group generated by topologically slice knots and let CD be the subgroup generated by knots with trivial Alexander polynomial. We prove the quotient CT/CD is infinitely generated, and uncover similar structure in the 3-dimensional rational spin bordism group. Our methods also lead to the construction of links that are topologically, but not smoothly, concordant to boundary links.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.