714 research outputs found
Multivariable signatures, genus bounds and -solvable cobordisms
We refine prior bounds on how the multivariable signature and the nullity of
a link change under link cobordisms. The formula generalizes a series of
results about the 4-genus having their origins in the Murasugi-Tristram
inequality, and at the same time extends previously known results about
concordance invariance of the signature to a bigger set of allowed variables.
Finally, we show that the multivariable signature and nullity are also
invariant under -solvable cobordism.Comment: 41 pages, 3 figure
Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4
We find a graph of genus and its drawing on the orientable surface of
genus with every pair of independent edges crossing an even number of
times. This shows that the strong Hanani-Tutte theorem cannot be extended to
the orientable surface of genus . As a base step in the construction we use
a counterexample to an extension of the unified Hanani-Tutte theorem on the
torus.Comment: 12 pages, 4 figures; minor revision, new section on open problem
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