By considering a (not necessarily locally-flat) PL knot as the singular locus of a PL stratified pseudomanifold, we can use intersection homology theory to define intersection Alexander polynomials, a generalization of the classical Alexander polynomial invariants for smooth or PL locally-flat knots. We show that the intersection Alexander polynomials satisfy certain duality and normalization c...

Let M be a complete locally compact CAT(0)-space, and X an ultralimit of M . For γ ⊂M a k-dimensional flat, let γω be the k-dimensional flat in X obtained as an ultralimit of γ. In this paper, we identify various conditions on γω that are sufficient to ensure that γ bounds a (k + 1)-dimensional half-flat. As applications we obtain (1) constraints on the behavior of quasi-isometries between loca...

The local model fitting (LMF) method is a useful single-shot surface profiling algorithm based on spatial carrier frequency fringe patterns. The measurement principle of the LMF method relies on the assumption that the target surface is locally flat. In this paper, we first analyze the measurement error of the LMF method caused by violation of the locally flat assumption. More specifically, we ...

In quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle H over the space J of compatible complex structures on a symplectic vector space. This bundle is equipped with a projectively flat connection. We show that par...

We show that noncongruence subgroups of SL2(Z) projectively equivalent to congruence subgroups are ubiquitous. More precisely, they always exist if the congruence subgroup in question is a principal congruence subgroup Γ(N) of level N > 2, and they exist in many cases also for Γ0(N). The motivation for asking this question is related to modular forms: projectively equivalent groups have the sam...

We investigate the action of semigroups of d× d matrices with entries in the max-plus semifield on the max-plus projective space. Recall that semigroups generated by one element with projectively bounded image are projectively finite and thus contain idempotent elements. In terms of orbits, our main result states that the image of a minimal orbit by an idempotent element of the semigroup with m...