| 期刊全稱(chēng) | A Guide to the Classification Theorem for Compact Surfaces | | 影響因子2023 | Jean Gallier,Dianna Xu | | 視頻video | http://file.papertrans.cn/142/141013/141013.mp4 | | 發(fā)行地址 | Student-centred guide offering comprehensive—and comprehensible—treatment of the classification theorem for compact surfaces.A short proof using graph theory (due to Thomassen) that every compact surf | | 學(xué)科分類(lèi) | Geometry and Computing | | 圖書(shū)封面 |  | | 影響因子 | This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example..Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing e | | Pindex | Textbook 2013 |
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