DRAWINGS ON LANTERN SLIDES

The Histological Slides and Drawings of Cajal

Ramón y Cajal's studies in the field of neuroscience provoked a radical change in the course of its history. For this reason he is considered as the father of modern neuroscience. Some of his original preparations are housed at the Cajal Museum (Cajal Institute, CSIC, Madrid, Spain). In this article, we catalogue and analyse more than 4,500 of Cajal's histological preparations, the same prepara...

Slides on Approximation algorithms

A lantern lemma

We show that in the mapping class group of a surface any relation between Dehn twists of the form T j xT k y = M (M a multitwist) is the lantern relation, and any relation of the form (TxTy) k = M (where Tx commutes with M ) is the 2-chain relation. AMS Classification 57M07; 20F38, 57N05

Combining Problems on RAC Drawings and Simultaneous Graph Drawings

We present an overview of the first combinatorial results for the so-called geometric RAC simultaneous drawing problem (or GRacSim drawing problem, for short), i.e., a combination of problems on geometric RAC drawings [3] and geometric simultaneous graph drawings [2]. According to this problem, we are given two planar graphs G1 = (V,E1) and G2 = (V,E2) that share a common vertex set but have di...

Applications of the Lantern Identity

The purpose of this note is to unify the role of the lantern identity in the proof of several finiteness theorems. In particular, we show that for every nonnegative integer m, the vector space (over the rationals) of type m (resp. T -type m) invariants of integral homology 3-spheres are finite dimensional. These results have already been obtained by [Oh] and [GL2] respectively; our derivation h...