Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 26 for “"fundamental group"”.
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The Fundamental Group: A Geometric Perspective
… of metric geometry. We begin by constructing the fundamental group of a topological space, using the concept of loops and loop homotopy to identify a global topological invariant such as a hole or puncture. We then transition to the geometric realm of metric spaces and isometries, demonstrating …
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The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds
… in dimension 4. Using a known formula for the fundamental group of a compact orientable toric origami manifold, a list of all groups obtainable as the fundamental group of a compact orientable toric origami 4-manifold is given, along with example manifolds that realize them. The known …
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Homomorphisms into the Fundamental Group of One-Dimensional and Planar Peano Continua
… continuum. Let E be a Hawaiian Earring with fundamental group H. We show that every homomorphism from H to the fundamental group of X is conjugate to a homomorphism which is induced by a continuous function.
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Topological Complexity of Configuration Spaces
… the topological complexity of a space and its fundamental group, namely when the fundamental group is ”small”, i.e. either has small order or small cohomological dimension. We also apply the navigation functions technique introduced in [20] to the study of the topological complexity of …
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Visualizing Geometric Structures on Topological Surfaces
… internal measures unchanged. The language of groups gives us a way to distinguish geometric structures. Understanding the mapping class group is an important and hard problem. This paper contributes to visualizing how the mapping class group acts on geometric structures. We explore the …
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Galois representations of orthogonal rigid local systems
… to continuous representations of the etale fundamental group, which can be specialized to compatible systems of Galois representations. This leads to the second maximally unipotent family. Because of the geometric origin, we can show using a theorem of Barnet-Lamb, Gee, Geraghty and Taylor …
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Infinite Product Group
… been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied …
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Two Aspects of Topology in Graph Configuration Spaces
… spaces are closely related to classical braid groups, which can be described as fundamental groups of configuration spaces of points in the plane. We examine this relationship by finding a presentation for the fundamental group of one graph configuration space.
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Homotopy mapping spaces
<p>In algebraic topology, one studies the group structure of sets of homotopy classes of maps (such as the homotopy groups pin( X)) to obtain information about the spaces in question. It is also possible to place natural topologies on these groups that remember local properties ignored by the …
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Some combinatorial aspects in algebraic topology and geometric group theory
… self-contained dissertation on the theory of the fundamental group and of the coverings. Finally, there are some recent problems in geometric group theory which are related to the presence of finitely presented groups which appear naturally as fundamental groups.
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Coverings and Descent Theory of Finite Spaces
… finite topological space and the actions of the fundamental group of that space. Since some descent theory is necessary for categorical Galois theory, this thesis also contains an account of some of the descent theory of finite topological spaces. The reader is assumed to know the basics of …
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Cohomology Jumping Loci and the Relative Malcev Completion
Two standard invariants used to study the fundamental group of the complement X of a hyperplane arrangement are the Malcev completion of its fundamental group G and the cohomology groups of X with coefficients in rank one local systems. In this thesis, we develop a tool that unifies these two …
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A family of biaffine geometries and their resulting amalgams
… We give two pairs of examples with ag-transitive groups, which lead to amalgam results for recognising either one of \(q\)\(^6\) : \(SU\)\(_3\)\((q)\) or \(G\)\(_2\)\((q)\), or one of \(q\)\(^7\) : \(G\)\(_2\)\((q)\) or \(Spin\)\(^7\)\((q)\). Also, we give details of a computer program to …
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Cubical small-cancellation theory and large-dimensional hyperbolic groups
Given a finitely presented group Q and a compact special cube complex X with nonelementary hyperbolic fundamental group, we produce a non-elementary, torsion-free, cocompactly cubulated hyperbolic group Γ that surjects onto Q, with kernel isomorphic to a quotient of G = π_1X and such that …
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Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles
… field k of characteristic 2 with automorphism group Z/2Z × S_3, there exist SL(2,k[[s]])-representations of π_1(X) such that the image of π_1(X^-) is infinite. This result produces a family of examples similar to Laszlo's counterexample [Las01] to a question regarding the finiteness of the …
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Computing Interesting Topological Features
Finally, we examine a more fundamental homotopy problem in a different setting. A Rips complex is a simplicial complex defined by a set of points from some metric space where every pair of points within distance 1 is connected by an edge, and every (k + 1)-clique in that graph forms a k-simplex. We …
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Geometric, Algebraic, and Topological Connections in the Historical Sphere of the Platonic Solids
… interpretation of the icosians, a non-abelian group that describes certain "passages" between faces of the Platonic solids; and in Henri Poincaré's <italic>Analysis</italic> <italic>situs</italic>, in which 0- and 1-dimensional homology are determined. Incidentally, Poincaré's …
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Higher-order polynomial invariants of 3-manifolds giving lower bounds for Thurston norm
… of invariants, d&d1;n for n ≥ 0, of a group G that measure the size of the successive quotients of the derived series of G. In the case that G is the fundamental group of a 3-manifold, we obtain new 3-manifold invariants. These invariants are closely related to the topology of the …
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