Existing methods manage to reduce the maximal possible number of critical vertices, but increase thereby the number of regular vertices. In the case of non-Abelian Chern-Simons theories, the relevant one-form symmetry is non-invertible, and its “gauging” corresponds to the condensation of a Lagrangian anyon. GEOMETRIC topology has quite a few books that present its modern essentials to graduate student readers - the books by Thurston, Kirby and Vassiliev come to mind - but the vast majority of algebraic topology texts are mired in material that was old when Ronald Reagan was President of The United States. So put on your big boy pants and stop wasting your time looking into lesser books hoping they will be easier to understand. In this book the authors present the technical tools needed for proving rigorously the classification theorem, give a detailed proof using these tools, and also discuss the history of the theorem and its various proofs.

The kinds of course notes I have in mind are ones that introduce or cover some big modern topic, rather than ones which are geared to proving one theorem. He covers much more information than any of the other introductory textbooks I have perused, and with tons of explicitly worked out examples.Algebraic topoligy books that emphasize geometrical intuition usually have only a modest technical reach. I took one course that used this text and it was hell, but now I'm studying it on my own at a more leisurely pace. So, as a follow-up to first-year algebraic topology - still far from the cutting edge, but very relevant to reaching it - may I recommend reading some of the classic papers of the mid-twentieth century? I know of one careless mistake every reader will catch and one subtle mistake almost no reader will catch). Note: The superscript * denotes a missing solution, a partial solution, or a solution that’s wrong and has yet to be corrected.

Sometimes when the definition of a term is supplied (such as for "open simplex"), it will be immediately abused and applied to other things without comment that are not really the same thing (such as happens with "open simplex") -- thus causing countless hours of needless confusion. One or more similar collections would be useful for future developments, but I feel that Alg Top is much too big now to be contained adequately in a single text.A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. By bidding on, or purchasing this item, you are agreeing to us sharing your name and address details with that 3rd party supplier to allow us to fulfil our contractual obligations to you. The finished book apparently bears little resemblance to the draft lecture note versions that have been circulating the internet for a few years now.

I slightly take issue with the exercises not being self-contained and requiring material not presented to solve with rigor.Covers classical topics related to the vector field problem, the EHP sequence, and Adams's work on Im(J). But still, at the end of the day, even though it's often the case that when I add the details to a one page proof by Hatcher it becomes a five page proof (such as for Theorem 2. This book is worth its weight in gold just for all the examples both throughout the text and in the exercises. For example, CW complexes have proved over time to be the most natural class of spaces for algebraic topology, so they are emphasized here much more than in the books of an earlier generation. Charles Rezk only did some reformatting/writing which affected large parts of the post so that he got assigned the largest share of the CW post and thus shows up prominently.