Homotopy theory with Bornological coarse spaces. (2020)
- Record Type:
- Book
- Title:
- Homotopy theory with Bornological coarse spaces. (2020)
- Main Title:
- Homotopy theory with Bornological coarse spaces
- Further Information:
- Note: Ulrich Bunke, Alexander Engel.
- Other Names:
- Bunke, Ulrich, 1963-
Engel, Alexander - Contents:
- Intro -- Contents -- 1 Introduction -- Part I Motivic Coarse Spaces and Spectra -- 2 Bornological Coarse Spaces -- 2.1 Basic Definitions -- 2.2 Examples -- 2.3 Categorical Properties of BornCoarse -- 3 Motivic Coarse Spaces -- 3.1 Descent -- 3.2 Coarse Equivalences -- 3.3 Flasque Spaces -- 3.4 u-Continuity and Motivic Coarse Spaces -- 3.5 Coarse Excision and Further Properties -- 4 Motivic Coarse Spectra -- 4.1 Stabilization -- 4.2 Further Properties of Yo-s -- 4.3 Homotopy Invariance -- 4.4 Axioms for a Coarse Homology Theory -- 5 Merging Coarse and Uniform Structures 5.1 The Hybrid Structure -- 5.2 Decomposition Theorem -- 5.2.1 Uniform Decompositions and Statement of the Theorem -- 5.2.2 Proof of the Decomposition Theorem -- 5.2.3 Excisiveness of the Cone-at-Infinity -- 5.3 Homotopy Theorem -- 5.3.1 Statement of the Theorem -- 5.3.2 Proof of the Homotopy Theorem -- 5.3.3 Uniform Homotopies and the Cone Functors -- 5.4 Flasque Hybrid Spaces -- 5.5 Decomposition of Simplicial Complexes -- 5.5.1 Metrics on Simplicial Complexes -- 5.5.2 Decomposing Simplicial Complexes -- 5.6 Flasqueness of the Coarsening Space -- 5.6.1 Construction of the Coarsening Space 5.6.2 Flasqueness for the C0-Structure -- 5.6.3 Flasqueness for the Hybrid Structure -- 5.7 The Motivic Coarse Spectra of Simplicial Complexes and Coarsening Spaces -- Part II Coarse and Locally Finite Homology Theories -- 6 First Examples and Comparison of Coarse Homology Theories -- 6.1 Forcing u-Continuity -- 6.2Intro -- Contents -- 1 Introduction -- Part I Motivic Coarse Spaces and Spectra -- 2 Bornological Coarse Spaces -- 2.1 Basic Definitions -- 2.2 Examples -- 2.3 Categorical Properties of BornCoarse -- 3 Motivic Coarse Spaces -- 3.1 Descent -- 3.2 Coarse Equivalences -- 3.3 Flasque Spaces -- 3.4 u-Continuity and Motivic Coarse Spaces -- 3.5 Coarse Excision and Further Properties -- 4 Motivic Coarse Spectra -- 4.1 Stabilization -- 4.2 Further Properties of Yo-s -- 4.3 Homotopy Invariance -- 4.4 Axioms for a Coarse Homology Theory -- 5 Merging Coarse and Uniform Structures 5.1 The Hybrid Structure -- 5.2 Decomposition Theorem -- 5.2.1 Uniform Decompositions and Statement of the Theorem -- 5.2.2 Proof of the Decomposition Theorem -- 5.2.3 Excisiveness of the Cone-at-Infinity -- 5.3 Homotopy Theorem -- 5.3.1 Statement of the Theorem -- 5.3.2 Proof of the Homotopy Theorem -- 5.3.3 Uniform Homotopies and the Cone Functors -- 5.4 Flasque Hybrid Spaces -- 5.5 Decomposition of Simplicial Complexes -- 5.5.1 Metrics on Simplicial Complexes -- 5.5.2 Decomposing Simplicial Complexes -- 5.6 Flasqueness of the Coarsening Space -- 5.6.1 Construction of the Coarsening Space 5.6.2 Flasqueness for the C0-Structure -- 5.6.3 Flasqueness for the Hybrid Structure -- 5.7 The Motivic Coarse Spectra of Simplicial Complexes and Coarsening Spaces -- Part II Coarse and Locally Finite Homology Theories -- 6 First Examples and Comparison of Coarse Homology Theories -- 6.1 Forcing u-Continuity -- 6.2 Additivity and Coproducts -- 6.2.1 Additivity -- 6.2.2 Coproducts -- 6.3 Coarse Ordinary Homology -- 6.4 Coarsification of Stable Homotopy -- 6.4.1 Rips Complexes and a Coarsification of Stable Homotopy -- 6.4.2 Proof of Theorem 6.32 6.4.3 Further Properties of the Functor Q and Generalizations -- 6.5 Comparison of Coarse Homology Theories -- 7 Locally Finite Homology Theories and Coarsification -- 7.1 Locally Finite Homology Theories -- 7.1.1 Topological Bornological Spaces -- 7.1.2 Definition of Locally Finite Homology Theories -- 7.1.3 Additivity -- 7.1.4 Construction of Locally Finite Homology Theories -- 7.1.5 Classification of Locally Finite Homology Theories -- 7.2 Coarsification of Locally Finite Theories -- 7.3 Analytic Locally Finite K-Homology -- 7.3.1 Extending Functors from Locally Compact Spaces to TopBorn 7.3.2 Cohomology for Cstar-Algebras -- 7.3.3 Locally Finite Homology Theories from Cohomology Theories for Cstar-Algebras -- 7.4 Coarsification Spaces -- 8 Coarse K-Homology -- 8.1 X-Controlled Hilbert Spaces -- 8.2 Ample X-Controlled Hilbert Spaces -- 8.3 Roe Algebras -- 8.4 K-Theory of C*-Algebras -- 8.5 C*-Categories and Their K-Theory -- 8.5.1 Definition of Cstar-Categories -- 8.5.2 From Cstar-Categories to Cstar-Algebras and K-Theory -- 8.5.3 K-Theory Preserves Filtered Colimits -- 8.5.4 K-Theory Preserves Unitary Equivalences -- 8.5.5 Exactness of K-Theory -- 8.5.6 Additivity of K-Theory … (more)
- Publisher Details:
- Cham : Springer
- Publication Date:
- 2020
- Extent:
- 1 online resource
- Subjects:
- 514/.24
Homotopy theory
Bornological spaces
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9783030513351
3030513351 - Related ISBNs:
- 3030513343
9783030513344 - Notes:
- Note: Includes bibliographical references and index.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.550468
- Ingest File:
- 03_167.xml