From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10638 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: A book on Algebraic Topology Date: Mon, 10 Jan 2022 18:27:45 +0100 Message-ID: Reply-To: Marco Grandis Mime-Version: 1.0 (Mac OS X Mail 14.0 \(3654.120.0.1.13\)) Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="5460"; mail-complaints-to="usenet@ciao.gmane.io" To: categories list Original-X-From: majordomo@rr.mta.ca Wed Jan 12 23:20:36 2022 Return-path: Envelope-to: gsmc-categories@m.gmane-mx.org Original-Received: from smtp2.mta.ca ([198.164.44.75]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1n7lyu-0001Ej-Mk for gsmc-categories@m.gmane-mx.org; Wed, 12 Jan 2022 23:20:36 +0100 Original-Received: from rr.mta.ca ([198.164.44.159]:41114) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1n7lz6-0004QG-Ex; Wed, 12 Jan 2022 18:20:48 -0400 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1n7lxd-0007bi-FL for categories-list@rr.mta.ca; Wed, 12 Jan 2022 18:19:17 -0400 Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10638 Archived-At: This new book is an introduction to Algebraic Topology, structurally = based on Homological Algebra and Category Theory: =20 Marco Grandis Algebraic Topology, A Structural Introduction World Scientific Publishing Company, 2022, x + 362 pages https://www.worldscientific.com/worldscibooks/10.1142/12586 Downloadable Introduction: https://www.worldscientific.com/doi/epdf/10.1142/9789811248368_0001 Presentation Algebraic Topology is a system and strategy of partial translations, = aiming to reduce difficult topological problems to algebraic facts that = can be more easily solved. The main subject of this book is singular = homology, the simplest of these translations. Studying this theory and = its applications, we also investigate its underlying structural layout - = the topics of Homological Algebra, Homotopy Theory and Category Theory = which occur in its foundation. This book is an introduction to a complex domain, with references to its = advanced parts and ramifications. It is written with a moderate amount = of prerequisites =E2=80=94 basic general topology and little else =E2=80=94= and a moderate progression starting from a very elementary beginning. A = consistent part of the exposition is organised in the form of exercises, = with suitable hints and solutions. It can be used as a textbook for a semester course or self-study, and a = guidebook for further study. Contents: =E2=80=A2 Preface =E2=80=A2 Introduction =E2=80=A2 Introducing Algebraic Topology =E2=80=A2 Singular Homology =E2=80=A2 Relative Singular Homology and Homology Theories =E2=80=A2 Singular Homology with Coefficients =E2=80=A2 Derived Functors, Universal Coefficients and = Products =E2=80=A2 An Introduction to Homotopy Groups =E2=80=A2 Complements on Categories and Topology =E2=80=A2 Solutions to the Exercises =E2=80=A2 References =E2=80=A2 Index Marco Grandis e-mail: grandis@dima.unige.it http://www.dima.unige.it/~grandis/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]