The Coxeter Quotient of the Fundamental Group of a Galois Cover of 𝕋 × 𝕋

2006 â—˝  
Vol 34 (1) â—˝  
pp. 89-106 â—˝  
Author(s):  
Meirav Amram â—˝  
Mina Teicher â—˝  
Uzi Vishne
Keyword(s):  
Fundamental Group â—˝  
Galois Cover

THE FUNDAMENTAL GROUP OF THE GALOIS COVER OF HIRZEBRUCH SURFACE F1(2, 2)

2007 â—˝  
Vol 17 (03) â—˝  
pp. 507-525 â—˝  
Author(s):  
MEIRAV AMRAM â—˝  
MINA TEICHER â—˝  
UZI VISHNE
Keyword(s):  
Fundamental Group â—˝  
Hirzebruch Surface â—˝  
Generic Projection â—˝  
Galois Cover â—˝  
Hirzebruch Surfaces â—˝  
Galois Covers â—˝  
Branch Curve

This paper is the second in a series of papers concerning Hirzebruch surfaces. In the first paper in this series, the fundamental group of Galois covers of Hirzebruch surfaces Fk(a, b), where a, b are relatively prime, was shown to be trivial. For the general case, the conjecture stated that the fundamental group is [Formula: see text] where c = gcd (a, b) and n = 2ab + kb2. In this paper, we degenerate the Hirzebruch surface F1(2, 2), compute the braid monodromy factorization of the branch curve in â„‚2, and verify that, in this case, the conjecture holds: the fundamental group of the Galois cover of F1(2, 2) with respect to a generic projection is isomorphic to [Formula: see text].

THE FUNDAMENTAL GROUP OF GALOIS COVER OF THE SURFACE đť•‹ Ă— đť•‹

2008 â—˝  
Vol 18 (08) â—˝  
pp. 1259-1282 â—˝  
Author(s):  
MEIRAV AMRAM â—˝  
MINA TEICHER â—˝  
UZI VISHNE
Keyword(s):  
Fundamental Group â—˝  
Dimensional Torus â—˝  
One Dimensional â—˝  
Generic Projection â—˝  
Galois Cover â—˝  
The One â—˝  
First Time

This is the final paper in a series of four, concerning the surface đť•‹ Ă— đť•‹ embedded in â„‚â„™8, where đť•‹ is the one-dimensional torus. In this paper we compute the fundamental group of the Galois cover of the surface with respect to a generic projection onto â„‚â„™2, and show that it is nilpotent of class 3. This is the first time such a group is presented as the fundamental group of a Galois cover of a surface.

scholarly journals Fundamental group of Galois covers of degree 6 surfaces

2021 â—˝  
pp. 1-21
Author(s):  
M. Amram â—˝  
C. Gong â—˝  
U. Sinichkin â—˝  
S.-L. Tan â—˝  
W.-Y. Xu â—˝  
...  
Keyword(s):  
Fundamental Group â—˝  
Algebraic Surfaces â—˝  
Fundamental Groups â—˝  
Galois Cover â—˝  
Chern Numbers â—˝  
Galois Covers

In this paper, we consider the Galois covers of algebraic surfaces of degree 6, with all associated planar degenerations. We compute the fundamental groups of those Galois covers, using their degeneration. We show that for 8 types of degenerations, the fundamental group of the Galois cover is non-trivial and for 20 types it is trivial. Moreover, we compute the Chern numbers of all the surfaces with this type of degeneration and prove that the signatures of all their Galois covers are negative. We formulate a conjecture regarding the structure of the fundamental groups of the Galois covers based on our findings.

Calculating the Fundamental Group of Galois Cover of the (2,3)-embedding of â„‚â„™1 Ă— T

2020 â—˝  
Vol 36 (3) â—˝  
pp. 273-291
Author(s):  
Meirav Amram â—˝  
Sheng Li Tan â—˝  
Wan Yuan Xu â—˝  
Michael Yoshpe
Keyword(s):  
Fundamental Group â—˝  
Galois Cover

scholarly journals The fundamental group of a Galois cover of â„‚â„™1Ă—T

2002 â—˝  
Vol 2 (1) â—˝  
pp. 403-432 â—˝  
Author(s):  
Meirav Amram â—˝  
David Goldberg â—˝  
Mina Teicher â—˝  
Uzi Vishne
Keyword(s):  
Fundamental Group â—˝  
Galois Cover

Filling words in fundamental groups of Riemann surfaces

2013 â—˝  
Vol 50 (1) â—˝  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface â—˝  
Fundamental Group â—˝  
Riemann Surfaces â—˝  
Fundamental Groups â—˝  
Closed Geodesics â—˝  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 â—˝  
Author(s):  
Ahmed Abbes â—˝  
Michel Gros
Keyword(s):  
Fundamental Group â—˝  
Koszul Complex â—˝  
Finiteness Conditions â—˝  
Inverse Systems â—˝  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

scholarly journals TOPOLOGICAL 4-MANIFOLDS WITH 4-DIMENSIONAL FUNDAMENTAL GROUP

2021 â—˝  
pp. 1-8
Author(s):  
DANIEL KASPROWSKI â—˝  
MARKUS LAND
Keyword(s):  
Fundamental Group â—˝  
Homotopy Equivalent â—˝  
Poincaré Duality â—˝  
Poincare Duality â—˝  
Canonical Map â—˝  
Duality Space â—˝  
Simply Connected Manifolds â—˝  
Simply Connected â—˝  
Poincaré Duality Space

Abstract Let $\pi$ be a group satisfying the Farrell–Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$ has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby–Siebenmann invariant. If $\pi$ is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby–Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel’s conjecture, and simply connected manifolds where rigidity is a consequence of Freedman’s classification results.

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