LEADER 05231oam 2200541 450 001 996418200603316 005 20210415152203.0 010 $a981-15-5562-1 024 7 $a10.1007/978-981-15-5562-6 035 $a(CKB)4100000011508817 035 $a(DE-He213)978-981-15-5562-6 035 $a(MiAaPQ)EBC6380836 035 $a(PPN)257359559 035 $a(EXLCZ)994100000011508817 100 $a20210415d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aKuranishi structures and virtual fundamental chains /$fKenji Fukaya [and three others] 205 $a1st ed. 2020. 210 1$aSingapore :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XV, 638 p. 149 illus., 34 illus. in color.) 225 1 $aSpringer Monographs in Mathematics 311 $a981-15-5561-3 320 $aIncludes bibliographical references and index. 327 $a1.Introduction -- 2.Notations and conventions -- 3.Kuranishi structure and good coordinate system -- 4.Fiber product of Kuranishi structures -- 5.Thickening of a Kuranishi structure -- 6.Multivalued perturbation -- 7.CF-perturbation and integration along the fiber (pushout) -- 8.Stokes' formula -- 9.From good coordinate system to Kuranishi structure and back with CF-perturbations -- 10.Composition formula of smooth correspondences -- 11.Construction of good coordinate system -- 12.Construction of CF-perturbations -- 13.Construction of multivalued perturbations -- 14.Zero and one dimensional cases via multivalued perturbation -- 15.Introduction to Part 2 -- 16.Linear K-system: Floer cohomology I: statement -- 17.Extension of Kuranishi structure and its perturbation from boundary to its neighborhood -- 18.Smoothing corners and composition of morphisms -- 19.Linear K-system: Floer cohomology II: proof -- 20.Linear K-system: Floer cohomology III: Morse case by multisection -- 21.Tree-like K-system: A1 structure I: statement -- 22.Tree-like K-system: A1 structure II: proof -- 23. Orbifold and orbibundle by local coordinate -- 24.Covering space of effective orbifold and K-space -- 25.Admissible Kuranishi structure -- 26.Stratified submersion to a manifold with corners -- 27.Local system and smooth correspondence in de Rham theory with twisted coefficients -- 28.Composition of KG and GG embeddings: Proof of Lemma 3.34 -- 29.Global quotient and orbifold. . 330 $aThe package of Gromov?s pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including mirror symmetry and Hamiltonian dynamics. The Kuranishi structure was introduced by two of the authors of the present volume in the mid-1990s to apply this machinery on general symplectic manifolds without assuming any specific restrictions. It was further amplified by this book?s authors in their monograph Lagrangian Intersection Floer Theory and in many other publications of theirs and others. Answering popular demand, the authors now present the current book, in which they provide a detailed, self-contained explanation of the theory of Kuranishi structures. Part I discusses the theory on a single space equipped with Kuranishi structure, called a K-space, and its relevant basic package. First, the definition of a K-space and maps to the standard manifold are provided. Definitions are given for fiber products, differential forms, partitions of unity, and the notion of CF-perturbations on the K-space. Then, using CF-perturbations, the authors define the integration on K-space and the push-forward of differential forms, and generalize Stokes' formula and Fubini's theorem in this framework. Also, ?virtual fundamental class? is defined, and its cobordism invariance is proved. Part II discusses the (compatible) system of K-spaces and the process of going from ?geometry? to ?homological algebra?. Thorough explanations of the extension of given perturbations on the boundary to the interior are presented. Also explained is the process of taking the ?homotopy limit? needed to handle a system of infinitely many moduli spaces. Having in mind the future application of these chain level constructions beyond those already known, an axiomatic approach is taken by listing the properties of the system of the relevant moduli spaces and then a self-contained account of the construction of the associated algebraic structures is given. This axiomatic approach makes the exposition contained here independent of previously published construction of relevant structures. . 410 0$aSpringer monographs in mathematics. 606 $aGeometry, Differential 606 $aGeometry, Hyperbolic 606 $aPolytopes 606 $aCohomology operations 615 0$aGeometry, Differential. 615 0$aGeometry, Hyperbolic. 615 0$aPolytopes. 615 0$aCohomology operations. 676 $a516.36 700 $aFukaya$b Kenji$f1959-$0858007 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a996418200603316 996 $aKuranishi structures and virtual fundamental chains$92547514 997 $aUNISA LEADER 01463nam0 2200313 i 450 001 VAN0055984 005 20240125032155.584 010 $a978-05-215-5830-3 100 $a20061115d1995 |0itac50 ba 101 $aeng 102 $aGB 105 $a|||| ||||| 200 1 $aAlgebraic set theory$fA. Joyal, I. Moerdijk 210 $aCambridge$cCambridge university$d1995 215 $aVIII, 123 p.$d23 cm 410 1$1001VAN0029528$12001 $aLondon Mathematical Society lecture notes series$1210 $aCambridge$cCambridge university.$v220 606 $a03G30$xCategorical logic, topoi [MSC 2020]$3VANC024384$2MF 606 $a03E70$xNonclassical and second-order set theories [MSC 2020]$3VANC024419$2MF 620 $dCambridge$3VANL000024 700 1$aJoyal$bAndré$3VANV044463$0350839 701 1$aMoerdijk$bIeke$3VANV043068$059494 712 $aCambridge university $3VANV107986$4650 801 $aIT$bSOL$c20240126$gRICA 856 4 $uhttps://books.google.it/books?id=E0Xhn32xzZAC&pg=PA9&dq=9780521558303&hl=it&sa=X&ved=0ahUKEwi5vp7h9ZvcAhVKthQKHXW2AiEQ6AEIJzAA#v=onepage&q=9780521558303&f=false$zPreview 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $aVAN0055984 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08PREST 03-XX 2120 $e08 996 I 20061115 996 $aAlgebraic set theory$91424646 997 $aUNICAMPANIA LEADER 02286nam0 22004933i 450 001 VAN0274789 005 20240618124841.11 017 70$2N$a9783030909512 100 $a20240411d2021 |0itac50 ba 101 $aeng 102 $aCH 105 $a|||| ||||| 200 1 $aGeometric Approximation Theory$fAlexey R. Alimov, Igor? G. Tsar?kov 210 $aCham$cSpringer$d2021 215 $axxi, 508 p.$cill.$d24 cm 410 1$1001VAN0030486$12001 $aSpringer monographs in mathematics$1210 $aBerlin [etc.]$cSpringer 606 $a46B20$xGeometry and structure of normed linear spaces [MSC 2020]$3VANC019996$2MF 606 $a41A65$xAbstract approximation theory (approximation in normed linear spaces and other abstract spaces) [MSC 2020]$3VANC021234$2MF 606 $a41A46$xApproximation by arbitrary nonlinear expressions; widths and entropy [MSC 2020]$3VANC022009$2MF 606 $a41-XX$xApproximations and expansions [MSC 2020]$3VANC022010$2MF 606 $a54C60$xSet-valued maps in general topology [MSC 2020]$3VANC022295$2MF 606 $a54C65$xSelections in general topology [MSC 2020]$3VANC022296$2MF 606 $a41A28$xSimultaneous approximation [MSC 2020]$3VANC037833$2MF 610 $aBest approximation$9KW:K 610 $aChebyshev center$9KW:K 610 $aChebyshev set$9KW:K 610 $aChebyshev subspace$9KW:K 610 $aJung constant$9KW:K 610 $aMetric projection$9KW:K 610 $aNearest point$9KW:K 610 $aSun$9KW:K 610 $aWidth$9KW:K 620 $aCH$dCham$3VANL001889 700 1$aAlimov$bAlexey R.$3VANV227227$01733338 701 1$aTsar?kov$bIgor? G.$3VANV227228$01733339 712 $aSpringer $3VANV108073$4650 801 $aIT$bSOL$c20240621$gRICA 856 4 $uhttps://doi.org/10.1007/978-3-030-90951-2$zE-book ? Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o Shibboleth 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $fN 912 $aVAN0274789 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08CONS e-book 8243 $e08eMF8243 20240430 996 $aGeometric Approximation Theory$94149057 997 $aUNICAMPANIA