Sentence examples for fundamental groups with from inspiring English sources

The first exposition of foundational material on the arithmetic of fundamental groups with respect to the Section Conjecture of anabelian Geometry: from the history of the subject to the state of the art of the conjecture.

The aim of this book is to study various geometric properties and algebraic invariants of smooth projective varieties with infinite fundamental groups.

Let Y, (Y') be two projective manifolds with isomorphic fundamental groups.

It is proved that there exist factors of type II with different countable fundamental groups and hence, different actions.

Plant and Microbial Biology Plant Seminar: "What makes the Lyme disease bacterium tick?" We explain what connections and curvature have to do with representations of fundamental groups, and what instanton Floer homology or, more generally, instanton gauge theory, has to do with all this.

Hain, R, and Matsumoto, M. "Tannakian Fundamental Groups Associated to Galois Groups". Galois Groups and Fundamental Groups.

Then induces a homomorphism between fundamental groups.

Given an exact sequence ( 1 rightarrow pi _g rightarrow pi rightarrow pi _b rightarrow 1) where (g ge 3 ), (b ge 2), does there exist a Kodaira fibred surface S with fundamental group (pi )? (Le Brun's question, see [109]) : are there Kodaira fibred surfaces with slope ( c_1^2 / c_2 > 8/3)?

(1) Given an exact sequence ( 1 rightarrow pi _g rightarrow pi rightarrow pi _b rightarrow 1) where (g ge 3 ), (b ge 2), does there exist a Kodaira fibred surface S with fundamental group (pi )?   (2) (Le Brun's question, see [109]) : are there Kodaira fibred surfaces with slope ( c_1^2 / c_2 > 8/3)?   (3) Are there surfaces admitting three different Kodaira fibrations?  .

Consider a compact locally symmetric space M of rank r, with fundamental group Γ.

These manifolds are simply connected, hence by van Kampen we introduce the relation ( R_j x) = 1), and finally one obtains a M with fundamental group (cong Gamma ).