LEADER 00873nam0-2200313---450 001 990008168600403321 005 20200728104448.0 010 $a88-8382-091-6 035 $a000816860 035 $aFED01000816860 035 $a(Aleph)000816860FED01 035 $a000816860 100 $a20050721d2003----km-y0itay50------ba 101 0 $aita 102 $aIT 105 $aaf------001yy 200 1 $aJosé Antonio Coderch$ela cellula e la luce$fLuigi Spinelli 210 $aTorino$cTesto & Immagine$d2003 215 $a93 p.$cill.$d19 cm 225 1 $aUniversale di architettura$v134 610 0 $aCoderch, José Antonio 700 1$aSpinelli,$bLuigi$0299158 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990008168600403321 952 $aA 285 CAN$b3986 URB$fDARPU 959 $aDARPU 996 $aJosé Antonio Coderch$9736496 997 $aUNINA LEADER 06054nam 22005655 450 001 9910520062303321 005 20251113204242.0 010 $a3-030-84138-3 024 7 $a10.1007/978-3-030-84138-6 035 $a(MiAaPQ)EBC6838872 035 $a(Au-PeEL)EBL6838872 035 $a(CKB)20275201300041 035 $a(OCoLC)1292355484 035 $a(PPN)259384763 035 $a(DE-He213)978-3-030-84138-6 035 $a(EXLCZ)9920275201300041 100 $a20211201d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEquivariant Cohomology of Configuration Spaces Mod 2 $eThe State of the Art /$fby Pavle V. M. Blagojevi?, Frederick R. Cohen, Michael C. Crabb, Wolfgang Lück, Günter M. Ziegler 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (217 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2282 311 08$a3-030-84137-5 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Notation -- Contents -- 1 Snapshots from the History -- 1.1 The Braid Group -- 1.2 The Fundamental Sequence of Fibrations -- 1.3 Artin's Presentation of Bn and ?1(F(R2,n)) -- 1.4 The Cohomology Ring H*(F(R2,n) -- Z) -- 1.5 The Cohomology of the Braid Group Bn -- 1.6 The Cohomology Ring H*(Bn -- F2) -- 1.7 Cohomology of Braid Spaces -- 1.8 Homology of Unordered Configuration Spaces -- Part I Mod 2 Cohomology of Configuration Spaces -- 2 The Ptolemaic Epicycles Embedding -- 3 The Equivariant Cohomology of Pe(Rd ,2m) -- 3.1 Small Values of m -- 3.2 The Case m=2 -- 3.3 Cohomology of (XX)Z2Sd-1 and (XX)Z2EZ2 -- 3.4 The Induction Step -- 3.5 The Restriction Homomorphisms - Three Aspects -- 3.5.1 A Restriction Homomorphism and the Mùi Invariants -- 3.5.2 A Restriction Homomorphism and the Dickson Invariants -- 3.5.3 Two Lemmas -- 4 Hu'ng's Injectivity Theorem -- 4.1 Critical Points in Hu'ng's Proof of His Injectivity Theorem -- 4.2 Proof of the Injectivity Theorem -- 4.2.1 Prerequisites -- 4.2.2 Proof of the Dual Epimorphism Theorem -- 4.3 An Unexpected Corollary -- 4.3.1 Motivation -- 4.3.2 Corollary -- Part II Applications to the (Non-)Existence of Regular and Skew Embeddings -- 5 On Highly Regular Embeddings: Revised -- 5.1 k-Regular Embeddings -- 5.2 -Skew Embeddings -- 5.3 k-Regular-Skew Embeddings -- 5.4 Complex Highly Regular Embeddings -- 6 More Bounds for Highly Regular Embeddings -- 6.1 Examples of S2m-Representations and Associated Vector Bundles -- 6.1.1 Examples of S2m-Representations -- 6.1.2 Associated Vector Bundles -- 6.2 The Key Lemma and its Consequences -- 6.3 Additional Bounds for the Existence of Highly Regular Embeddings -- 6.4 Additional Bounds for the Existence of Complex Highly Regular Embeddings -- Part III Technical Tools -- 7 Operads -- 7.1 Definition and Basic Example -- 7.2 O-Space. 327 $a7.3 Little Cubes Operad -- 7.4 Cd-Spaces, An Example -- 7.5 Cd-Spaces, a Free Cd-Space Over X -- 7.6 Araki-Kudo-Dyer-Lashof Homology Operations -- 8 The Dickson Algebra -- 8.1 Rings of Invariants -- 8.2 The Dickson Invariants as Characteristic Classes -- 9 The Stiefel-Whitney Classes of the Wreath Square of a Vector Bundle -- 9.1 The Wreath Square and the (d-1)-Partial Wreath Square of a Vector Bundle -- 9.2 Cohomology of B(S2?)=S2B(?) -- 9.3 The Total Stiefel-Whitney Class of the Wreath Square of a Vector Bundle -- 10 Miscellaneous Calculations -- 10.1 Detecting Group Cohomology -- 10.2 The Image of a Restriction Homomorphism -- 10.3 Weyl Groups of an Elementary Abelian Group -- 10.4 Cohomology of the Real Projective Space with Local Coefficients -- 10.5 Homology of the Real Projective Space with Local Coefficients -- References -- Index. 330 $aThis book gives a brief treatment of the equivariant cohomology of the classical configuration space F(?^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F(?^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper. This invalidates a paper by three of the authors, Blagojevi?, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and ?-skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker. Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2282 606 $aAlgebraic topology 606 $aManifolds (Mathematics) 606 $aAlgebraic Topology 606 $aManifolds and Cell Complexes 615 0$aAlgebraic topology. 615 0$aManifolds (Mathematics) 615 14$aAlgebraic Topology. 615 24$aManifolds and Cell Complexes. 676 $a514.23 700 $aBlagojevic?$b Pavle V. M.$01075385 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910520062303321 996 $aEquivariant cohomology of configuration spaces Mod 2$92909883 997 $aUNINA