On additivity of centralisers

Remarks on Cyclic Additivity

Centralisers of Involutions in Black Box Groups

We discuss basic structural properties of finite black box groups. A special emphasis is made on the use of centralisers of involutions in probabilistic recognition of black box groups. In particular, we suggest an algorithm for finding the p-core of a black box group of odd characteristic. This special role of involutions suggest that the theory of black box groups reproduces, at a non-determi...

Comments on Hastings’ Additivity Counterexamples

3 Background on random states and channels 7 3.1 Probability distributions for states . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Probability distributions on the simplex ∆d . . . . . . . . . . . . . . . . . . . . . . 8 3.3 Estimates for μd,n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Probability distribution for random unitary channels . ....

On the additivity of knot width

It has been conjectured that the geometric invariant of knots in 3–space called the width is nearly additive. That is, letting w(K) ∈ 2N denote the width of a knot K ⊂ S , the conjecture is that w(K#K ) = w(K) + w(K ) − 2. We give an example of a knot K1 so that for K2 any 2–bridge knot, it appears that w(K1#K2) = w(K1), contradicting the conjecture. AMS Classification 11Y16, 57M50; 57M25

Additivity and non-additivity for perverse signatures

A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifolds with boundary. Wall showed that this property is not true of signatures on...