Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

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Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

Written by S. Cappell
4.85 95,189 ratings
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About this ebook:
Many phenomena of three-manifolds are related to the representations of their fundamental groups. The authors of this book, using an investigation of the intersections of Lagrangian subvarieties in singular symplectic varieties, develop invariants associated with the more general Lie group, including SU(n). From a combinatorial approach related to Vassiliev's perspective on knot theory, a number of researchers have obtained a theory of "finite-type invariants" of three-manifolds. The authors show that their general representation-theoretic invariants are of the finite type. As a result, their invariants have surgery formulae and are intimately related to issues in mapping class groups, knot theory and quantum physics. On the other hand, some combinatorial invariants are given new geometrical meaning through these relations with the fundamental group.

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Pages 200
Published October 1, 1999
ISBN 2498534
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S. Cappell
About the Author
S. Cappell

S. Cappell is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, S. Cappell can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Michael Jackson
Michael Jackson March 03, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Joseph Wilson
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes.
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Jennifer Walker October 06, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
George Wilson
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Donald Allen
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Nancy Scott
Nancy Scott April 14, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Sarah Gonzalez
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Nancy Parker December 09, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Ryan Williams
Ryan Williams May 30, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
George Nelson
George Nelson October 15, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Edward Adams
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Karen Collins
Karen Collins May 13, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Joseph Carter
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Jennifer Carter
Jennifer Carter March 21, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Paul Reyes
Paul Reyes May 04, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Sandra Garcia
Sandra Garcia June 07, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Mark Torres
Mark Torres February 16, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Stephanie Thomas
Stephanie Thomas March 01, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Margaret  Davis
Margaret Davis December 04, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Richard Thompson
Richard Thompson July 02, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Paul Smith
Paul Smith April 27, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Michael Moore
Michael Moore April 11, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Ashley Hernandez
Ashley Hernandez October 27, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
George Gonzalez
George Gonzalez September 21, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Rebecca Walker
Rebecca Walker April 12, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Laura Robinson
Laura Robinson February 21, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
William Brown
William Brown September 18, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Steven Walker
Steven Walker July 26, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Joseph Nelson
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
William Carter
William Carter April 22, 2025
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
Rebecca Williams
Rebecca Williams June 05, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Thomas Clark
Thomas Clark December 27, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Amanda Smith
Amanda Smith November 21, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Jennifer Nguyen
Jennifer Nguyen August 17, 2024
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Eric Rodriguez
Eric Rodriguez August 13, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Paul Thompson
Paul Thompson February 14, 2024
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
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