Primer mapping class groups
WebThis chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups. It first considers the classification of elements for the torus of Mod( T ² before discussing higher-genus analogues for each of the three types of elements of Mod( T ². WebAfter giving the definition, we compute the mapping class group in essentially all of the cases where it can be computed directly. This includes the case of the disk, the annulus, …
Primer mapping class groups
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http://euclid.nmu.edu/~joshthom/Teaching/MA589/farbmarg.pdf Web3. Natural actions of the mapping class group Expanded versions of many arguments in this section can be found in the Primer [FM12, Chapter 2 and 8]. The only difference is that, in Chapter 2, the Primer uses the standard mapping class group. The extended mapping class group MCG± of a surface Sis defined as the group of self-
http://euclid.nmu.edu/~joshthom/Teaching/MA589/farbmarg.pdf WebOct 10, 2014 · A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary (relatively) hyperbolic groups, CAT(0) groups with rank 1 elements, mapping class groups and Out(F n).As an application, we show that mapping class …
WebThis chapter explains the basics of the mapping class group of a surface. It first provides the definition and examples before computing the mapping class group in essentially all … WebThe study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance.It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained.
WebJul 18, 2024 · The Alexander Method in Farb and Maraglit's "A Primer on Mapping Class Groups" (p.59) (roughly) ... Later on in the book, they use this result to prove Fricke's theorem, namely that the action of the Mapping Class Group on Teichmüller space is properly discontinuous.
WebThe book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. booker\u0027s true barrel bourbonWebJun 15, 2024 · A Primer on Mapping Class Groups (Princeton Mathematical Series, 49). Princeton University Press, Princeton, NJ, 2012.Google Scholar [Gol20] Goldman, W.. Parallelism on Lie groups and Fox’s free differential calculus. god of war fill rage meterWebSep 26, 2011 · A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod (S), from finite generation by Dehn twists and low … god of war film complet en françaisWebApr 14, 2024 · I have a question concerning the proof of the - quote - "simple" lemma 3.16 in the "Primer on Mapping Class Groups" by Farb and Margalit. At first glance, the statement seemed very intuitive to me, but then, when reading through the provided proof, two questions popped up in my mind. The lemma reads: god of war figurkyWebStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange booker\u0027s turkey crownWebA primer on mapping class groups. Benson Farb, D. Margalit. Published 2013. Mathematics. Given a compact connected orientable surface S there are two fundamental objects … booker\\u0027s uncut and unfiltered reviewWebNov 11, 2024 · We get improvements in their stability results, which for the spin mapping class groups we show to be optimal away from the prime $2$. We also prove that in both cases the $\mathbb{F}_2$-homology satisfies secondary homological stability. god of war film 2022