Topological characterization of Bott map on $\mathrm{BU}$

A topological proof of Bott periodicity theorem and a characterization of BU

Bott Periodicity in Topological, Algebraic and Hermitian K-theory

This paper is devoted to classical Bott periodicity, its history and more recent extensions in algebraic and Hermitian K-theory. However, it does not aim at completeness. For instance, the variants of Bott periodicity related to bivariant K-theory are described by Cuntz in this handbook. As another example, we don’t emphasize here the relation between motivic homotopy theory and Bott periodicit...

Topological Map Merging

When multiple robots cooperatively explore an environment, maps from individual robots must be merged to produce a single globally consistent map. This is a difficult problem when the robots do not have a common reference frame or global positioning. In this paper, we describe an algorithm for merging embedded topological maps. Topological maps provide a concise description of the navigability ...

Mixed Topological Map

We propose a new algorithm which is based on a topological map model and dedicated to mixed data, with numerical and binary components. The algorithm computes directly the referent vectors, as mixed data vectors sharing the same interpretation with the observations. The method is validated on a real data related to the ocean colour domain.

TOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...