001449754 000__ 04905cam\a2200565\i\4500
001449754 001__ 1449754
001449754 003__ OCoLC
001449754 005__ 20230310004416.0
001449754 006__ m\\\\\o\\d\\\\\\\\
001449754 007__ cr\cn\nnnunnun
001449754 008__ 220925s2022\\\\sz\a\\\\ob\\\\001\0\eng\d
001449754 019__ $$a1345584490
001449754 020__ $$a9783031087059$$q(electronic bk.)
001449754 020__ $$a3031087054$$q(electronic bk.)
001449754 020__ $$z9783031087042
001449754 020__ $$z3031087046
001449754 0247_ $$a10.1007/978-3-031-08705-9$$2doi
001449754 035__ $$aSP(OCoLC)1345580913
001449754 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCQ
001449754 049__ $$aISEA
001449754 050_4 $$aQA565
001449754 08204 $$a516.3/52$$223/eng/20221004
001449754 1001_ $$aErlandsson, Viveka,$$eauthor.
001449754 24510 $$aMirzakhani's curve counting and geodesic currents /$$cViveka Erlandsson, Juan Souto.
001449754 264_1 $$aCham :$$bBirkhäuser,$$c[2022]
001449754 264_4 $$c©2022
001449754 300__ $$a1 online resource (xii, 226 pages) :$$billustrations.
001449754 336__ $$atext$$btxt$$2rdacontent
001449754 337__ $$acomputer$$bc$$2rdamedia
001449754 338__ $$aonline resource$$bcr$$2rdacarrier
001449754 4901_ $$aProgress in mathematics ;$$vvolume 345
001449754 504__ $$aIncludes bibliographical references and index.
001449754 5050_ $$6880-01$$aIntro -- Preface -- Acknowledgments -- Contents -- Notation -- 1 Introduction -- Some Things that the Reader Will Not Find in This Book -- What the Reader Will Find Here -- A Comment on the Way This Book Is Written -- 2 Read Me -- Curves, Multicurves, and Arcs -- Intersection Number -- Geodesic Representatives -- Random Geodesics. Or Length Versus Intersections -- Space of Geodesics -- Geodesics Projecting into a Fixed Compact Set -- Laminations -- Hausdorff Limits -- Mapping Class Group -- Shortening Curves -- 3 Geodesic Currents -- Definition and Examples -- Curves as Currents
001449754 5058_ $$aMasur's Ergodicity Theorem -- An Example: The Case of the Once Punctured Torus -- Comments -- Piecewise Linear Structure -- Symplectic Structure -- Weil-Petersson Volume Form -- Other Interesting Measures on ML(S) -- 5 Radallas -- Terminology -- The Game of Cars -- Almost Geodesic Radallas -- Finding Almost Geodesic Radallas -- Generic Curves -- Comments: Expected Angle of Self-Intersection -- 6 Subconvergence of Measures -- Idea of the Proof of Theorem 6.1 -- Local Map -- Global Map -- New Measures -- Comments -- 7 Approximating the Thurston Measure -- Dribbling
001449754 506__ $$aAccess limited to authorized users.
001449754 520__ $$aThis monograph presents an approachable proof of Mirzakhanis curve counting theorem, both for simple and non-simple curves. Designed to welcome readers to the area, the presentation builds intuition with elementary examples before progressing to rigorous proofs. This approach illuminates new and established results alike, and produces versatile tools for studying the geometry of hyperbolic surfaces, Teichmuller theory, and mapping class groups. Beginning with the preliminaries of curves and arcs on surfaces, the authors go on to present the theory of geodesic currents in detail. Highlights include a treatment of cusped surfaces and surfaces with boundary, along with a comprehensive discussion of the action of the mapping class group on the space of geodesic currents. A user-friendly account of train tracks follows, providing the foundation for radallas, an immersed variation. From here, the authors apply these tools to great effect, offering simplified proofs of existing results and a new, more general proof of Mirzakhanis curve counting theorem. Further applications include counting square-tiled surfaces and mapping class group orbits, and investigating random geometric structures. Mirzakhanis Curve Counting and Geodesic Currents introduces readers to powerful counting techniques for the study of surfaces. Ideal for graduate students and researchers new to the area, the pedagogical approach, conversational style, and illuminating illustrations bring this exciting field to life. Exercises offer opportunities to engage with the material throughout. Basic familiarity with 2-dimensional topology and hyperbolic geometry, measured laminations, and the mapping class group is assumed.
001449754 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 4, 2022).
001449754 650_0 $$aCurves.
001449754 650_0 $$aCurves, Algebraic.
001449754 655_0 $$aElectronic books.
001449754 7001_ $$aSouto, Juan,$$eauthor.
001449754 77608 $$iPrint version: $$z3031087046$$z9783031087042$$w(OCoLC)1319076631
001449754 77608 $$iPrint version:$$aErlandsson, Viveka.$$tMirzakhani's curve counting and geodesic currents.$$dCham : Springer, 2022$$z9783031087042$$w(OCoLC)1338652988
001449754 830_0 $$aProgress in mathematics (Boston, Mass.) ;$$vv. 345.
001449754 852__ $$bebk
001449754 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-08705-9$$zOnline Access$$91397441.1
001449754 909CO $$ooai:library.usi.edu:1449754$$pGLOBAL_SET
001449754 980__ $$aBIB
001449754 980__ $$aEBOOK
001449754 982__ $$aEbook
001449754 983__ $$aOnline
001449754 994__ $$a92$$bISE