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- Title
Concordance crosscap number of a knot.
- Abstract
We define the concordance crosscap number γc(K) of a knot K as the minimum crosscap number among all the knots concordant to K. The four-dimensional crosscap number γ*(K) is the minimum first Betti number of non-orientable surfaces smoothly embedded in the four-dimensional ball, bounding the knot K. Clearly, γ*(K) ≤ γc(K). We construct two infinite sequences of knots for which γ*(K) < γc(K). In particular, the knot 74 is one of the examples.
- Subjects
CONCORDANCES (Topology); KNOT theory; EMBEDDINGS (Mathematics); INFINITE series (Mathematics); NUMBER theory; ALGEBRA
- Publication
Bulletin of the London Mathematical Society, 2007, Vol 39, Issue 5, p755
- ISSN
0024-6093
- Publication type
Article
- DOI
10.1112/blms/bdm058