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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


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