On the concept of genus in topology and complex analysis.

*(English)*Zbl 1171.57300From the introduction: The English word “genus” hails from biology, where it is used to connote a grouping of organisms having common characteristics. In mathematics the word is also used to group objects with common characteristics. The concept of genus arises in various mathematical contexts, such as number theory, as well as in the areas we consider in this article, topology and complex analysis. Even within the latter two areas there are various notions of genus that historically originated with the genus of an oriented surface. We begin with these origins and afterward treat generalizations and modifications. We provide no detailed definitions and proofs; rather, our goal is to give the reader an intuitive feeling for the concept of genera.

##### MSC:

57-02 | Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes |

32-02 | Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces |

55-02 | Research exposition (monographs, survey articles) pertaining to algebraic topology |