2003/11/09 by Mikami Hirasawa, Hirasawa, Mikami, Lee Rudolph +1
Mathematics · #57M25 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0311134
23 figures; supercedes, and considerably extends, mathGT/0108006
arxiv created 2003/11/09 · openalex publication_date 2003/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Morse-Novikov number MN(L) of an oriented link L in the 3-sphere is the minimum number of critical points of a Morse map from the complement of L in the 3-sphere to the circle representing the class of a Seifert surface for L (e.g., the Morse-Novikov number of L is zero if and only if L is fibered). We develop various constructions of Morse maps (Milnor maps, Stallings twists, splicing along a link which is a closed braid with respect to a Morse map, Murasugi sums, cutting a Morse map along an arc on a page) and use them to bound Morse-Novikov numbers from above in terms of other knot and link invariants (free genus, crossing number, braid index, wrapping genus and layered wrapping genus).