LEADER 02847nam 22005895 450 001 9910483912603321 005 20251113174229.0 010 $a3-030-51335-1 024 7 $a10.1007/978-3-030-51335-1 035 $a(CKB)4100000011413850 035 $a(DE-He213)978-3-030-51335-1 035 $a(MiAaPQ)EBC6336359 035 $a(PPN)250220482 035 $a(EXLCZ)994100000011413850 100 $a20200903d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHomotopy Theory with Bornological Coarse Spaces /$fby Ulrich Bunke, Alexander Engel 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (VII, 245 p. 71 illus., 3 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2269 311 08$a3-030-51334-3 320 $aIncludes bibliographical references and index. 330 $aProviding a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories. It introduces the category of bornological coarse spaces and the notion of a coarse homology theory, and further constructs the universal coarse homology theory. Hybrid structures are introduced as a tool to connect large-scale with small-scale geometry, and are then employed to describe the coarse motives of bornological coarse spaces of finite asymptotic dimension. The remainder of the book is devoted to the construction of examples of coarse homology theories, including an account of the coarsification of locally finite homology theories and of coarse K-theory. Thereby it develops background material about locally finite homology theories and C*-categories. The book is intended for advanced graduate students and researchers who want to learn about the homotopy-theoretical aspects of large scale geometry via the theory of infinity categories. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2269 606 $aK-theory 606 $aGeometry 606 $aAlgebraic topology 606 $aK-Theory 606 $aGeometry 606 $aAlgebraic Topology 615 0$aK-theory. 615 0$aGeometry. 615 0$aAlgebraic topology. 615 14$aK-Theory. 615 24$aGeometry. 615 24$aAlgebraic Topology. 676 $a514.24 676 $a514.24 700 $aBunke$b Ulrich$4aut$4http://id.loc.gov/vocabulary/relators/aut$0791284 702 $aEngel$b Alexander$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483912603321 996 $aHomotopy Theory with Bornological Coarse Spaces$92391154 997 $aUNINA