Simplicial Structures in Topology

1. Front Matter

   Pages i-xvi

   PDF

2. Fundamental Concepts

   • Davide L. Ferrario, Renzo A. Piccinini

   Pages 1-41

3. The Category of Simplicial Complexes

   • Davide L. Ferrario, Renzo A. Piccinini

   Pages 43-97

4. Homology of Polyhedra

   • Davide L. Ferrario, Renzo A. Piccinini

   Pages 99-149

5. Cohomology

   • Davide L. Ferrario, Renzo A. Piccinini

   Pages 151-169

6. Triangulable Manifolds

   • Davide L. Ferrario, Renzo A. Piccinini

   Pages 171-193

7. Homotopy Groups

   • Davide L. Ferrario, Renzo A. Piccinini

   Pages 195-237

8. Back Matter

   Pages 239-243

   PDF

Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The last chapter of the book is devoted to homotopy groups, which are used in short introduction on obstruction theory. The text is more in tune with the original development of algebraic topology as given by Henry Poincaré (singular homology is discussed). Illustrative examples throughout and extensive exercises at the end of each chapter for practice enhance the text. Advanced undergraduate and beginning graduate students will benefit from this book. Researchers and professionals interested in topology and applications of mathematics will also find this book useful.

From the reviews:

“The book under review is a modern and enlightened exposition of those finite combinatorial structures and of the simplicial algebraic topology … . Ferrario (Univ. di Milano-Bicocca, Italy) and Piccinini (Dalhousie Univ., Canada) aim to develop the simplicial homology and cohomology of finite simplicial complexes, and of their geometric realizations … with an eye to reaching the classification theory for compact 2-mainfolds. … The foreword, preface, exercises, references, and index all add value to the book. Summing Up: Recommended. Academic audiences; upper-division undergraduates and above.” (F. E. J. Linton, Choice, Vol. 48 (11), August, 2011)

“This book is about the topology of finite simplicial structures … . The book is generally well-written … . One of the main strengths of the book lies in plenty of motivating discussion and explanation, with good use of examples. There are plenty of exercises at the ends of most chapter sections. In summary, this is good text for advanced undergraduate students and beginning graduate students in topology. It is potentially useful as a source of project topics for undergraduate students.”­­­ (Sarah Whitehouse, CMS Notes, Vol. 43 (5), October-November, 2011)

“The authors … aim is essentially to expound upon Poincare’s fundamental contributions to the subject of topology. … the content in this book could be a good choice for an upper-level undergraduate who would like to learn the basic ideas of algebraic topology without going into the technical details of singular homology. Even more advanced students, especially combinatorially-minded ones, might find it to be helpful. … this book has an interesting development in content that has not appeared elsewhere and should be a useful resource.” (Julia Bergner, Mathematical Reviews, Issue 2012 a)

“This book on algebraic topology is interesting and can be a basis for a course on homologicalalgebra or on homotopy theory or for a course on cellular structures in topology. It is a clear and comprehensive introduction to simplicial structures in topology with illustrative examples throughout and extensive exercises at the end of each chapter. This book is also a very good text for advanced undergraduate and beginning graduate students, researchers and professionals interested in topology and applications in mathematics.” (Corina Mohorianu, Zentralblatt MATH, Vol. 1211, 2011)

• Dipto. Matematica e Applicazioni, Università Milano-Bicocca, Milano, Italy

  Davide L. Ferrario

• Dept. Mathematics & Statistics, Dalhousie University, Halifax, Canada

  Renzo A. Piccinini

R.A. Piccinini: B.Sc. Universidade de S. Paulo (Brazil); Ph.D. The University of Wisconsin-Madison (USA). Professor: University of S.Paulo, Memorial University (Canada), Universita` di Milano (Italy), Universita` di Milano-Bicocca (Italy). Adjunct Professor: Dalhousie University (Canada). D.L. Ferrario: B.Sc. And PhD in Mathematics, University of Milano (Italy). Associate professor of Geometry at the University of Milano-Bicocca. Italy.

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