One-Cocycles and Knot Invariants is about classical knots, i.e., smooth oriented knots in 3-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used to construct combinatorial 1-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and the longitude of the knot. The combinatorial 1-cocycles are therefore lifts of the well-known Conway polynomial of knots, and they can be calculated in polynomial time. The 1-cocycles can distinguish loops consisting of knot diagrams in the moduli space up to homology. They give knot invariants when they are evaluated on canonical loops in the connected components of the moduli space. They are a first candidate for numerical knot invariants which can perhaps distinguish the orientation of knots.
Readership: This title will be particularly useful for academic researchers and PhD students.
azaanzahid2007 –
How many times you used this product? 12
“One-Cocycles and Knot Invariants serves as an exceptional gateway into the fascinating realm of modern knot theory. As Book 73 in the esteemed Series on Knots and Everything, it masterfully blends rigorous mathematics with clear motivation, leading readers from foundational concepts to powerful invariants with ease. The author presents one-cocycles in an elegant yet practical maner, demonstrating how abstract ideas can yield concrete topological understanding. The examples are carefully selected, proofs are succinct, and the broader implications are consistently highlightid. This volume is a must-read for both graduate students and researchers, as it fosters curiosity and enhances mathematical intuition through its engaging writing and enduring relevance.”
abdulhaseb403 –
How many times you used this product? 2
One-Cocycles and Knot Invariants is a detailed and insightful look into knot theory. The bok explains one-cocycles, invariants, and their importance in mathematics in a clear way, making it easier for advanced students and reserchers to understand complex ideas. It’s a great resource for those studying topology, providing clear explanations, examples, and thorough analysis within the field of knots.
df.wazir12 –
How many times you used this product? 1
Good
df.wazir12 –
How many times you used this product? 2
Nice product
u1b2a3i4d5u6ll7a8h9 –
How many times you used this product? 1
One-Cocycles and Knot Invariants is a detailed and insightful look into knot theory. The bok explains one-cocycles, invariants, and their importance in mathematics in a clear way, making it easier for advanced students and reserchers to understand complex ideas. It’s a great resource for those studying topology, providing clear explanations, examples, and thorough analysis within the field of knots.
m.shahzain0817 –
How many times you used this product? 1
One-Cocycles and Knot Invariants by Thomas Fiedler is an essential resource for those studying high-level mathematics. This book moves away from overly complex algebra, focusing instead on a more visual and diagram-based approach to understanding knots. By introducing “one-cocycles,” Fiedler provides a clearer way to identify and distinguish different knot shapes.
While it is written for researchers and advanced students, the clear structure makes these difficult topological concepts much more accessible. It is a brilliant, forward-thinking addition to any mathematics library, offering new tools for the next generation of topologists.
mahnoorpervaiz789 –
How many times have you used this product ? 1
Unlock cutting-edge insights into knot theory with One-Cocycles and Knot Invariants. This rigorou yet accessible volume bridges topology, geometry, and algabra, offering powerful tools, fresh perspectives, and deep results. Essential for researchers and advanced students seeking clarity, innovation, and inspiration in modern mathematical knot theory worldwide academic libraries and collections.
khurasan0000 –
How many times have you used this product ? 4
One-Cocycles and Knot Invariants (Series on Knots and Everything, Book 73) is a compelling addition for mathematicians and researchers passionate about knot theory and topology. The book presents deep, original insights into the role of one-cocycles in understanding knot invariants, blending rigorous mathematics with clear, structured explanations. As part of this respected series, it maintains a high academic standard while offering valuable perspectives for advanced study and research.
Ideal as both a reference anod a source of inspiration, this volume helps readers explore new connectionsee and deepen their understanding of modern knot theory with confidence and clarity.
yadavnikhil1786 –
How many time have you used this product ? 1
Honestly, this is a pretty niche book, but if you’re deep into knot theory, it’s a must have.
It dives into one-cocycles and how they link up with knot invariants in a way that’s actualy pretty fresh. The math is heavy—dont get me wrong—but the author does a decent job of breaking down complex stuff like the Alexander polynomial and how it conects to modern topology.
It’s part of the “Series on Knots and Everything,” which is usualy solid, and this one doesnt disapoint. Some parts are a bit densly packed and you might find a couple typos in the equations if you’re lookin closely, but the overall logic is sound. Great pick if you’re a grad student or a researcher tryin to find new ways to look at knot invariants. Definetly worth haveing on your shelf if this is your field.
vibewithkaif –
This book is outstanding the author’s treatment of one-cocycles and knot invariants is insightful and well-organized love that it provides a deep understanding of the subject matter a great resource for researchers and advanced students in topology
kumarkartik6626 –
How many time have you used this product ? 1
One-Cocycles and Knot Invariants is a solid and thoughtful contribution to the study of knot theory. The book dives into a specialized topic, but it does so in a clear and organized way that makes the material approachable for readers who already have some background in topology.
What I appreciated most is how the author connects abstract cohomological ideas to concrete knot invariants. The explanations are careful and precise, and the progression of ideas feels natural rather than rushed. Even when the mathematics becomes dense, the motivation behind the constructions is usually clear, which helps a lot when working through the details.
The examples and arguments are well chosen and highlight how one-cocycles play a meaningful role in understanding knot invariants, rather than feeling like purely theoretical exercises. This makes the book especially useful for graduate students and researchers who want to deepen their understanding of modern knot theory.
Overall, this is not a casual read, but it is a valuable reference and a rewarding one for anyone seriously interested in knot invariants and low-dimensional topology. Definitely worth adding to a specialized math library.
elassassino333 –
How many time have you used this product ? 1
A good book and can be recommended to everyone
mohdshahan047 –
How many time have you used this product ? 2
“Mind-blown! One-Cocycles and Knot Invariants is a masterclass in mathematical elegance. Perfect for knot theory enthusiasts and researchers Deep insights, brilliant exposition – a must-read in the field!”
sandhyalugun08 –
Book is so good
sandhyalugun08 –
Recommended for book lovers