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## Beyond characteristic classes

*Stanley Chang and Shmuel Weinberger*

### in Quantum Mechanics

- Published in print:
- 2019
- Published Online:
- May 2021
- ISBN:
- 9780691160498
- eISBN:
- 9780691200354
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691160498.003.0006
- Subject:
- Mathematics, Geometry / Topology

This chapter examines the existence of interesting manifolds using surgery. For finite fundamental groups, excellent examples are provided by the space form problem, the classification of topy lens ... More

## Topological Invariants and Differential Geometry

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number ... More

## Path Components and the Fundamental Group

*Graham Ellis*

### in An Invitation to Computational Homotopy

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198832973
- eISBN:
- 9780191871375
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198832973.003.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization, Geometry / Topology

This chapter introduces some of the basic concepts of algebraic topology and describes datatypes and algorithms for implementing them on a computer. The basic concepts include: regular CW-complex, ... More

## Facsimile : A p-adic Simpson correspondence

*Gerd Faltings*

### in The p-adic Simpson Correspondence (AM-193)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170282
- eISBN:
- 9781400881239
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170282.003.0007
- Subject:
- Mathematics, Algebra

This chapter presents the facsimile of Gerd Faltings' article entitled “A p-adic Simpson Correspondence,” reprinted from Advances in Mathematics 198(2), 2005. In this article, an equivalence between ... More

## Cohomology of Higgs isocrystals

*Takeshi Tsuji*

### in The p-adic Simpson Correspondence (AM-193)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170282
- eISBN:
- 9781400881239
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170282.003.0004
- Subject:
- Mathematics, Algebra

This chapter describes the cohomology of Higgs isocrystals, which are introduced to replace the notion of Higgs bundles. The link between these two notions uses Higgs envelopes and calls to mind the ... More

## Drinfeld’s lemma for diamonds

*Peter Scholze and Jared Weinstein*

### in Berkeley Lectures on p-adic Geometry: (AMS-207)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691202082
- eISBN:
- 9780691202150
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691202082.003.0016
- Subject:
- Mathematics, Geometry / Topology

This chapter addresses Drinfeld's lemma for diamonds. It proves a local analogue of Drinfeld's lemma, thereby giving a first nontrivial argument involving diamonds. This lecture is entirely about ... More

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