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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Classification of Compact 2-manifolds

Winslow, George H 01 January 2016 (has links)
It is said that a topologist is a mathematician who can not tell the difference between a doughnut and a coffee cup. The surfaces of the two objects, viewed as topological spaces, are homeomorphic to each other, which is to say that they are topologically equivalent. In this thesis, we acknowledge some of the most well-known examples of surfaces: the sphere, the torus, and the projective plane. We then observe that all surfaces are, in fact, homeomorphic to either the sphere, the torus, a connected sum of tori, a projective plane, or a connected sum of projective planes. Finally, we delve into algebraic topology to determine that the aforementioned surfaces are not homeomorphic to one another, and thus we can place each surface into exactly one of these equivalence classes.
2

Toroidal Embeddings and Desingularization

NGUYEN, LEON 01 June 2018 (has links)
Algebraic geometry is the study of solutions in polynomial equations using objects and shapes. Differential geometry is based on surfaces, curves, and dimensions of shapes and applying calculus and algebra. Desingularizing the singularities of a variety plays an important role in research in algebraic and differential geometry. Toroidal Embedding is one of the tools used in desingularization. Therefore, Toroidal Embedding and desingularization will be the main focus of my project. In this paper, we first provide a brief introduction on Toroidal Embedding, then show an explicit construction on how to smooth a variety with singularity through Toroidal Embeddings.
3

Quandles of Virtual Knots

Tamagawa, Sherilyn K 01 January 2014 (has links)
Knot theory is an important branch of mathematics with applications in other branches of science. In this paper, we explore invariants on a special class of knots, known as virtual knots. We find new invariants by taking quotients of quandles, and introducing the fundamental Latin Alexander quandle and its Grobner basis. We also demonstrate examples of computations of these invariants.
4

Der Wertvorrat der gemischten Inhalte von zwei, drei und vier ebenen Eibereichen

Heine, Rudolf, January 1937 (has links)
Thesis--Ernst-Moritz-Arndt-Universität, 1935. / Lebenslauf.
5

Finite Group Actions on the Four-Dimensional Sphere

Breton, Sacha 10 1900 (has links)
<p>Smith theory provides powerful tools for understanding the geometry of singular sets of group actions on spheres. In this thesis, tools from Smith theory and spectral sequences are brought together to study the singular sets of elementary abelian groups acting locally linearly on S4. It is shown that the singular sets of such actions are homeomorphic to the singular sets of linear actions. A short review of the literature on group actions on S4 is included.</p> / Master of Science (MSc)
6

The Inertia Group of Smooth 7-manifolds

Gollinger, William 04 1900 (has links)
<p>Let $\Theta_n$ be the group of $h$-cobordism classes of homotopy spheres, i.e. closed smooth manifolds which are homotopy equivalent to $S^n$, under connected sum. A homotopy sphere $\Sigma^n$ which is not diffeomorphic to $S^n$ is called ``exotic.'' For an oriented smooth manifold $M^n$, the {\bf inertia group} $I(M)\subset\Theta_n$ is defined as the subgroup of homotopy spheres such that $M\#\Sigma$ is orientation-preserving diffeomorphic to $M$. This thesis collects together a number of results on $I(M)$ and provides a summary of some fundamental results in Geometric Topology. The focus is on dimension $7$, since it is the smallest known dimension with exotic spheres. The thesis also provides two new results: one specifically about $7$-manifolds with certain $S^1$ actions, and the other about the effect of surgery on the homotopy inertia group $I_h(M)$.</p> / Master of Science (MSc)
7

Equivariant Gauge Theory and Four-Manifolds

Anvari, Nima 10 1900 (has links)
<p>Let $p>5$ be a prime and $X_0$ a simply-connected $4$-manifold with boundary the Poincar\'e homology sphere $\Sigma(2,3,5)$ and even negative-definite intersection form $Q_=\text_8$ . We obtain restrictions on extending a free $\bZ/p$-action on $\Sigma(2,3,5)$ to a smooth, homologically-trivial action on $X_0$ with isolated fixed points. It is shown that for $p=7$ there is no such smooth extension. As a corollary, we obtain that there does not exist a smooth, homologically-trivial $\bZ/7$-equivariant splitting of $\#^8 S^2 \times S^2=E_8 \cup_ \overline$ with isolated fixed points. The approach is to study the equivariant version of Donaldson-Floer instanton-one moduli spaces for $4$-manifolds with cylindrical ends. These are $L^2$-finite anti-self dual connections which asymptotically limit to the trivial product connection.</p> / Doctor of Philosophy (PhD)
8

Analysis of eigenvalues and conjugate heat kernel under the Ricci flow

Abolarinwa, Abimbola January 2014 (has links)
No description available.
9

Harmonic analysis in non-Euclidean geometry : trace formulae and integral representations

Awonusika, Richard Olu January 2016 (has links)
This thesis is concerned with the spectral theory of the Laplacian on non-Euclidean spaces and its intimate links with harmonic analysis and the theory of special functions. More specifically, it studies the spectral theory of the Laplacian on the quotients M = Γ\G/K and X = G/K, where G is a connected semisimple Lie group, K is a maximal compact subgroup of G and Γ is a discrete subgroup of G.
10

Bounds for complete arcs in finite projective planes

Pichanick, E. V. D. January 2016 (has links)
This thesis uses algebraic and combinatorial methods to study subsets of the Desarguesian plane IIq = PG(2, q). Emphasis, in particular, is given to complete (k, n)-arcs and plane projective curves. Known Diophantine equations for subsets of PG(2, q), no more than n of which are collinear, have been applied to k-arcs of arbitrary degree. This yields a new lower bound for complete (k, n)-arcs in PG(2, q) and is a generalization of a classical result of Barlotti. The bound is one of few known results for complete arcs of arbitrary degree and establishes new restrictions upon the parameters of associated projective codes. New results governing the relationship between (k, 3)-arcs and blocking sets are also provided. Here, a sufficient condition ensuring that a blocking set is induced by a complete (k, 3)-arc in the dual plane q is established and shown to complement existing knowledge of relationships between k-arcs and blocking sets. Combinatorial techniques analyzing (k, 3)-arcs in suitable planes are then introduced. Utilizing the numeric properties of non-singular cubic curves, plane (k, 3)-arcs satisfying prescribed incidence conditions are shown not to attain existing upper bounds. The relative sizes of (k, 3)-arcs and non-singular cubic curves are also considered. It is conjectured that m3(2, q), the size of the largest complete (k, 3)-arc in PG(2, q), exceeds the number of rational points on an elliptic curve. Here, a sufficient condition for its positive resolution is given using combinatorial analysis. Exploiting its structure as a (k, 3)-arc, the elliptic curve is then considered as a method of constructing cubic arcs and results governing completeness are established. Finally, classical theorems relating the order of the plane q to the existence of an elliptic curve with a specified number of rational points are used to extend theoretical results providing upper bounds to t3(2, q), the size of the smallest possible complete (k, 3)-arc in PG(2, q).

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