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　　黎曼麯麵及其模空間的概念由黎曼分彆在其博士畢業論文和一篇著名的文章中定義。由於與數學和物理的許多學科聯係廣泛，黎曼麯麵及其模空間得到瞭深入的研究，並將繼續吸引人們的關注。近期熱帶麯綫的研究迅速崛起。熱帶代數麯綫是經典復數域上代數麯綫以及黎曼麯麵在熱帶半環上的一種模擬。
　　《黎曼麯麵和熱帶麯綫的模空間導引（英文版）》深入淺齣地介紹瞭以上幾個重要數學分支，並且重點強調如代數幾何、復幾何、雙麯幾何、拓撲、幾何群理論和數學物理等不同學科之間的關聯。季理真是美國密歇根大學教授，研究興趣涉及幾何、拓撲和分析領域，以及這些領域之間的聯係，喜歡閱讀和寫作，曾獲得Sloan研究奬。
　　Eduard Looijenga是世界代數幾何學傢之一，荷蘭皇傢藝術和科學院院士，現任教於清華大學。

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前言/序言

　　analogy with locally symmetric spaces， which by definition are obtained as orbit space of symmetric spaces endowed with an action of an arithmetic group. This analogy， though imperfect， has been very fruitful in the past decades， as it suggested both problems and solutions.
　　As we mentioned， compact Riemann surfaces can also be regarded as algebraic curves over the complex numbers. In the past few years， there has been an explosion of work on their tropical counterparts， i.e.， algebraic curves over the tropical semifield. These have appeared in many unexpected topics and make currently a very active area of study. It turns out that the moduli spaces of tropical curves also fit into the above analogy，in the sense that these are the orbit spaces of tropical Teichmuller spaces by outer automorphism groups of free groups. The outer automorphism groups of free groups are among the most important groups in geometric group theory， and the tropical Teichmuller spaces were studied as spaces of marked metric graphs before the subject of tropical geometry （and its name） existed.
　　Given the rich history of Riemann surfaces and their moduli spaces， and their generalizations， applications and connections with other subjects， it seems helpful to provide an accessible and timely introduction to all the above topics， while emphasizing the underlying connections. The current book is an attempt towards this goal. It consists of two parts. The first part deals with mapping class groups of surfaces， Teichmuller spaces and their applications to moduli spaces of Riemann surfaces， whereas the second part deals with tropical analogues and some applications in geometric group theory. Though these parts were conceived independently， together they cover both basic and essential results in these subjects as well as some recent developments. Although there exist several works on some of the above topics， we hope and believe that the nature of the subject justifies our offering of our own perspective on this wonderful world.
黎曼麯麵和熱帶麯綫的模空間導引（英文版） [Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves] 下載 mobi epub pdf txt 電子書

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