2024 Primer on mapping class groups

Primer on mapping class groups

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August undefined, 2024

WebOct 16, 2011 · The 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. Along the way, central objects and tools are introduced, ... 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.

A primer on mapping class groups - Semantic Scholar

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 … WebThe group is the mapping class group of S, denoted by Mod(S). This group is defined by the isotopy classes of orientation-preserving homeomorphism from S to itself. Equivalently, Mod(S) may be defined using diffeomorphisms instead of homeomorphisms or homotopy classes instead of isotopy classes. The space is the Teichmüller space of S, Teich(S). hotel alpina st. johann alpendorf

A Primer on Mapping Class Groups (PMS-49) on JSTOR

WebOct 16, 2011 · The 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 … WebSep 10, 2015 · This provides an algebraic group structure on MCG, and the representation theory of algebraic groups is rich and elegant. I can go on forever, but I prefer to give you an excellent reference: A primer on mapping class groups, by Farb and Margalit. It develops in an accessible way everything I wrote and goes far beyond. WebNorthern Michigan University hotel altair misano

Primer on mapping class groups

Web"The 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 … WebA linear transformation of a vector space is determined by, and is best understood by, its action on vectors. In analogy with this, we shall see that an element of the mapping class …

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http://link.library.missouri.edu/portal/A-primer-on-mapping-class-groups-Benson-Farb-and/vnshhMBh47I/ WebNov 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 …

WebNov 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. WebJun 14, 2013 · The Primer gives a short, but very nice, introduction to these connections. Later chapters of the Primer develop connections between mapping class groups and …

WebFigure 11.7 An example of a surface obtained by gluing Euclidean rectangles by Euclidean translations. As with the Swiss cross example, this surface can be given the structure of a Riemann surface with a holomorphic quadratic differential. - "A …

WebThe Birman exact sequence: the forgetful map For this, we will consider the pure mapping class group PMCG(S). This is the subgroup of MCG(S) that xes each puncture of S. Let S = S g;p with p 1 and choose a puncture y. If we \forget" the puncture y we get the surface S g;p 1. Suppose that f is a mapping class in PMCG(S). Since f is a pure

WebIndex(−1, 1)-form3334g + 2 theorem20321184(g −12032109g − 9 theorem287439G-invariants of a group action364Sg-bundle over S1379Sg-tile273I(Sg)-equivalent186ǫ-thi hotel altaia alteaWebJul 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. hotel altair aliminiWebThe mapping class group of a surface is its group of homeomorphisms modulo isotopy. According to Benson Farb, “the appearance of mapping class groups in mathematics is ubiquitous.” Indeed, mapping class groups show up in fields including geometric group theory, symplectic geometry, algebraic geometry, and geometric and low-dimensional … hotel altamarea misanoWebDownload PDF - A Primer On Mapping Class Groups [PDF] [5c4ojgbmc220]. The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies … hotel al sana kolkataWebJan 1, 2011 · Benson Farb, Dan Margalit. 5.00. 7 ratings2 reviews. The study of the mapping class group Mod (S) is a classical topic that is experiencing a renaissance. It lies at the … hotel alsisar haveli jaipurWebAbstract. This book deals with two fundamental objects attached to a surface S and how they relate to each other: a group and a space. The group is the mapping hotel al tajolWebthe topology and geometry of S. Mapping class groups are ubiquitous, appearing in subjects as diverse as algebraic geometry, combinatorial group theory, symplectic geometry, ... hotel alta las palomas san jose