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覆蓋、對(duì)應(yīng)和非交換幾何(英文) 版權(quán)信息
- ISBN:9787560399157
- 條形碼:9787560399157 ; 978-7-5603-9915-7
- 裝幀:平裝-膠訂
- 冊(cè)數(shù):暫無
- 重量:暫無
- 所屬分類:>
覆蓋、對(duì)應(yīng)和非交換幾何(英文) 內(nèi)容簡介
本書是一部英文版的數(shù)學(xué)專著。本書內(nèi)容相當(dāng)艱深且小眾,估計(jì)只有少數(shù)研究者才會(huì)感興趣.但由于雅可比猜想是一個(gè)歷史感頗強(qiáng)的大猜想且至今無人解決,所以筆者相信一定會(huì)有人從收藏心態(tài)購買之。
覆蓋、對(duì)應(yīng)和非交換幾何(英文) 目錄
1.Introduction
Chapter 1.Graphs Category and Three-manifolds as correspondences
1.Three-manifolds as correspondences
2.Composition ofcorrespondencas
3.Representations and compositions of correspondences
4.Semigroupoids and additive categories
5.Categories of graphs and correspondences
6.Convolution algebra and time evolution
7.Equivalence of correspondences
8.Convolution algebras and 2-semigroupoids
9.Vertical and horizontal time evolutions
10.Vertical time evolution: Hattie-Hawking gravity
11.Vertical time evolution: gauge moduli and index theory
12.Horizontal time evolution: bivariant Chern character
13.Noncommutative spaces and spectral correspondences
Chapter 2.Knots, Khovanov Homology
1.Introduction
2.From graphs to knots
3.Khovanov Homology
4.Knots and Links Cobordism Groups
5.Graphs and cobordisms
6.Homology theories for embedded graphs
7.Questions and Future Work
Appendix A.
1.Branched Covering
2.Filtration
3.Knot and link
4.Topological Quantum Field Theory
5.2-Category
6.Group Rings
7.Creation and annihilation operators
8.A quick introduction to Dirac operators
9.Concepts of Cyclic Cohomology
Appendix.Bibliography
編輯手記
Chapter 1.Graphs Category and Three-manifolds as correspondences
1.Three-manifolds as correspondences
2.Composition ofcorrespondencas
3.Representations and compositions of correspondences
4.Semigroupoids and additive categories
5.Categories of graphs and correspondences
6.Convolution algebra and time evolution
7.Equivalence of correspondences
8.Convolution algebras and 2-semigroupoids
9.Vertical and horizontal time evolutions
10.Vertical time evolution: Hattie-Hawking gravity
11.Vertical time evolution: gauge moduli and index theory
12.Horizontal time evolution: bivariant Chern character
13.Noncommutative spaces and spectral correspondences
Chapter 2.Knots, Khovanov Homology
1.Introduction
2.From graphs to knots
3.Khovanov Homology
4.Knots and Links Cobordism Groups
5.Graphs and cobordisms
6.Homology theories for embedded graphs
7.Questions and Future Work
Appendix A.
1.Branched Covering
2.Filtration
3.Knot and link
4.Topological Quantum Field Theory
5.2-Category
6.Group Rings
7.Creation and annihilation operators
8.A quick introduction to Dirac operators
9.Concepts of Cyclic Cohomology
Appendix.Bibliography
編輯手記
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