LEADER 03616nam 2200481 450 001 9910813200603321 005 20220528001309.0 010 $a1-4704-4823-8 035 $a(CKB)4100000007133852 035 $a(MiAaPQ)EBC5571105 035 $a(Au-PeEL)EBL5571105 035 $a(OCoLC)1065248741 035 $a(RPAM)20649665 035 $a(PPN)231946414 035 $a(EXLCZ)994100000007133852 100 $a20220528d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCluster algebras and triangulated surfaces$hPart II$iLambda lenghts /$fSergey Fomin, Dylan Thurston 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2018] 210 4$dİ2018 215 $a1 online resource (110 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vVolume 255, number 1223 311 $a1-4704-2967-5 320 $aIncludes bibliographical references. 327 $aCover -- Title page -- Chapter 1. Introduction -- Chapter 2. Non-normalized cluster algebras -- Chapter 3. Rescaling and normalization -- Chapter 4. Cluster algebras of geometric type and their positive realizations -- Chapter 5. Bordered surfaces, arc complexes, and tagged arcs -- Chapter 6. Structural results -- Chapter 7. Lambda lengths on bordered surfaces with punctures -- Chapter 8. Lambda lengths of tagged arcs -- Chapter 9. Opened surfaces -- Chapter 10. Lambda lengths on opened surfaces -- Chapter 11. Non-normalized exchange patterns from surfaces -- Chapter 12. Laminations and shear coordinates -- Chapter 13. Shear coordinates with respect to tagged triangulations -- Chapter 14. Tropical lambda lengths -- Chapter 15. Laminated Teichmu?ller spaces -- Chapter 16. Topological realizations of some coordinate rings -- Chapter 17. Principal and universal coefficients -- Appendix A. Tropical degeneration and relative lambda lengths -- Appendix B. Versions of Teichmu?ller spaces and coordinates -- Bibliography -- Back Cover. 330 $aFor any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmu?ller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface. 410 0$aMemoirs of the American Mathematical Society ;$vVolume 255, number 1223. 606 $aCluster algebras 615 0$aCluster algebras. 676 $a512.44 700 $aFomin$b Sergey$01709536 702 $aThurston$b Dylan P.$f1972- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813200603321 996 $aCluster algebras and triangulated surfaces$94099356 997 $aUNINA LEADER 04774nam 22006255 450 001 9910746966703321 005 20251009083446.0 010 $a9783031341502 010 $a3031341503 024 7 $a10.1007/978-3-031-34150-2 035 $a(MiAaPQ)EBC30764551 035 $a(Au-PeEL)EBL30764551 035 $a(CKB)28443805900041 035 $a(DE-He213)978-3-031-34150-2 035 $a(EXLCZ)9928443805900041 100 $a20230929d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Invention of Infinity: Essays on Husserl and the History of Philosophy /$fby Claudio Majolino 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (387 pages) 225 1 $aContributions to Phenomenology, In Cooperation with The Center for Advanced Research in Phenomenology,$x2215-1915 ;$v124 311 08$aPrint version: Majolino, Claudio The Invention of Infinity: Essays on Husserl and the History of Philosophy Cham : Springer,c2023 9783031341496 327 $aIntroduction -- 1. The invention of infinity? On some provisional questions -- Part I: Openings -- 2. Multiplicity, manifolds and varieties of constitution. A manifesto -- 3. The reach of attitudes -- Part II: Maps -- 4. Individuum and region of being. On the unifying principle of a ?headless? ontology -- 5. Mapping ontology and its boundaries -- Part III: Worlds and Unworlds -- 6. ?Until the end of the world?. On eidetic variation and absolute being of consciousness -- 7. Within and beyond productive imagination. A historical-critical inquiry into phenomenology -- Part IV: Paths -- 8. The vicissitudes of the improper -- 9. Back to the meanings themselves (and away from the Noema). On phenomenology and the Stoic doctrine of the lekton -- Part V: Infinity -- 10. Plato?s light and Gorgias?s shadow. On the manifold ?beginnings? of philosophy -- 11. The Infinite Academy. On how to be a Platonist with some (Aristotelian?) help -- Conclusion -- 12. The invenvion of infinity. On a tentative answer. 330 $aThis book covers Husserl?s stance on the philosopher and the history of philosophy, whether or not such a history is part of the philosophical attitude itself, and if so, how Husserl?s phenomenology might weigh in on such matters. Firstly, this text spells out some of the manifold ways in which the history of philosophy works its way in Husserl?s phenomenology, showing how concepts, methods and problems drawn from various Ancient and Modern philosophical traditions (Platonism, Aristotelianism, Sophistry, Stoicism, Scholasticism, Modern Rationalism) are transformed and embedded within transcendental phenomenology itself. Secondly, it shows how a better understanding of the distinctive patterns by means of which Husserl?s phenomenology confronts the history of philosophy could be extremely significant for historians of philosophy who are interested in learning something entirely new about the unexplored horizons of such concepts, methods and problems. Finally, based on such twofoldhistorical and philosophical approach and thanks to a substantial reinterpretation of some key phenomenological concepts such as ?multiplicity?, ?constitution?, ?attitude? and ?variation?, this book provides a novel and original reading of Husserl?s overall philosophical project in its full meaning and scope. By doing so, this volume appeals to both students and researchers and critically engages in mainstream interpretations of phenomenology, suggesting a unique take on the idea of transcendental phenomenology as a whole. 410 0$aContributions to Phenomenology, In Cooperation with The Center for Advanced Research in Phenomenology,$x2215-1915 ;$v124 606 $aPhenomenology 606 $aPhilosophy$xHistory 606 $aReligion and sociology 606 $aPhilosophy, Modern 606 $aPhenomenology 606 $aHistory of Philosophy 606 $aPhenomenology of Religion 606 $aPhilosophical Traditions 615 0$aPhenomenology. 615 0$aPhilosophy$xHistory. 615 0$aReligion and sociology. 615 0$aPhilosophy, Modern. 615 14$aPhenomenology. 615 24$aHistory of Philosophy. 615 24$aPhenomenology of Religion. 615 24$aPhilosophical Traditions. 676 $a193 700 $aMajolino$b Claudio$01324034 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910746966703321 996 $aThe Invention of Infinity: Essays on Husserl and the History of Philosophy$94450870 997 $aUNINA