Local Homotopy Theory
The subject of this monograph is the homotopy theory of diagrams of spaces, chain complexes, spectra, and generalized spectra, where the homotopy types are determined locally by a Grothendieck topology. The main components of the theory are the local homotopy theories of simplicial presheaves an...
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
| Được phát hành: |
Springer
2015
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| Những chủ đề: | |
| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57251 |
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| Thư viện lưu trữ: | Thư viện Trường Đại học Đà Lạt |
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| Tóm tắt: | The subject of this monograph is the homotopy theory of diagrams of spaces,
chain complexes, spectra, and generalized spectra, where the homotopy types are
determined locally by a Grothendieck topology.
The main components of the theory are the local homotopy theories of simplicial
presheaves and simplicial sheaves, local stable homotopy theories, derived cate
gories, and non-abelian cohomology theory. This book presents formal descriptions
of the structures comprising these theories, and the links between them. Examples
and sample calculations are provided, along with some commentary.
The subject has broad applicability. It can be used to study presheaf and sheaf
objects which are defined on the open subsets of a topological space, or on the open
subschemes of a scheme, or on more exotic covers. Local homotopy theory is a
foundational tool for motivic homotopy theory, and for the theory of topological
modular forms in classical stable homotopy theory. As such, there are continuing
applications of the theory in topology, geometry, and number theory. The applications
and extensions of the subject comprise a large and expanding literature, in multiple
subject areas... |
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