This work has been of great interest both to topologists and to number theorists. The first part of this book describes some of the work of Kuo-Tsai Chen on iterated integrals and the fundamental group of a manifold. The author attempts to make his exposition accessible to beginning graduate students. He then proceeds to apply Chen's constructions to algebraic geometry, showing how this leads to some results on algebraic cycles and the Abel-Jacobi homomorphism. Finally, he presents a more general point of view relating Chen's integrals to a generalization of the concept of linking numbers, and ends up with a new invariant of homology classes in a projective algebraic manifold.
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... the first self contained introduction to this subject which is also adapted for non experts and graduate students. -- Zentralblatt MATH
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Inside This Book
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First Sentence:
Iterated integrals in calculus have the form. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
harmonic volume, iterated integrals, lower central series, algebraic cycles, homology class, flat connection, regularity theorem, period matrix, associative algebra, normal bundle, angular form, heat kernel, linking number New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Iterated integrals in calculus have the form. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
harmonic volume, iterated integrals, lower central series, algebraic cycles, homology class, flat connection, regularity theorem, period matrix, associative algebra, normal bundle, angular form, heat kernel, linking number New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 11
books:
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- Heat Kernels and Dirac Operators (Grundlehren Text Editions) by Nicole Berline in Front Matter, page 74, and Back Matter
- Algebraic K-Theory: Connections with Geometry and Topology (NATO Science Series C: (closed)) by John F. Jardine in Back Matter
- Scissors Congruences, Group Homology and Characteristic Classes (Nankai Tracts in Mathematics, V. 1.) by Johan L. Dupont in Front Matter
- Mathematics Unlimited by Björn Engquist in Back Matter
- Minimal Submanifolds and Related Topics (Nankai Tracts in Mathematics) by Yuanlong Xin in Front Matter
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