Unlinking information from 4-manifolds

We generalise theorems of Cochran-Lickorish and Owens-Strle to the case of links with more than one component. This enables the use of linking forms on double branched covers, Heegaard Floer correction terms, and Donaldson's diagonalisation theorem to complete the table of unlinking numbers for nonsplit prime links with crossing number nine or less.Comment: 18 pages, 2 figures. V2: Improved exposition incorporating referee's suggestions. Accepted for publication in Bull. London Math. So

Concordance group of virtual knots

We study concordance of virtual knots. Our main result is that a classical knot K is virtually slice if and only if it is classically slice. From this we deduce that the concordance group of classical knots embeds into the concordance group of long virtual knots

Multivariable signatures, genus bounds and 0.50.5-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 $0.5$-solvable cobordism.Comment: 41 pages, 3 figure

Anonymous Point Collection - Improved Models and Security Definitions

This work is a comprehensive, formal treatment of anonymous point collection. The proposed definition does not only provide a strong notion of security and privacy, but also covers features which are important for practical use. An efficient realization is presented and proven to fulfill the proposed definition. The resulting building block is the first one that allows for anonymous two-way transactions, has semi-offline capabilities, yields constant storage size, and is provably secure

Anonymous Point Collection - Improved Models and Security Definitions

This work is a comprehensive, formal treatment of anonymous point collection. The proposed definition does not only provide a strong notion of security and privacy, but also covers features which are important for practical use. An efficient realization is presented and proven to fulfill the proposed definition. The resulting building block is the first one that allows for anonymous two-way transactions, has semi-offline capabilities, yields constant storage size, and is provably secure