What is the Genus? / Lecture Notes in Mathematics Bd.2162 (PDF)

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“This book provides a fascinating—yet technically quite demanding—tour of the ideas and generalizations that feed into our modern conception of the genus. It should therefore serve as a useful starting point for historical and even philosophical investigations into past mathematical practice of forming and shaping concepts. It may also be useful in teaching advanced mathematical content with a view to historical development … .” (Henrik Kragh Sørensen, ISIS, Vol. 109 (2), June, 2018)
“This book is addressed to any person with a little knowledge of mathematics (such as an undergraduate student) who wants to get an idea of some of the most important concepts that arose in geometry and topology in the last couple of centuries: the author has made a commendable effort to explain all the more advanced concepts almost from scratch (but obviously this was not possible for the last chapter).” (Pietro De Poi, Mathematical Reviews, July, 2017)

“This clear book thoroughly covers the metamorphosis and theoretical significance of the genus by using several historical approaches that incorporate discussions related to analysis, algebraic geometry, number theory, and topology. … The book contains 20 figures and concludes with a list of 200 references and an index, which will help those who wish to delve into deeper studies. Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals.” (D. P. Turner, Choice, Vol. 54 (9), May, 2017)