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Trace diagrams, representations, and low-dimensional topology /Peterson, Elisha. January 2006 (has links)
Thesis (Ph. D.) -- University of Maryland, College Park, 2006. / Includes bibliographical references (leaves 117-119). Also available online.
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Homotopy string links over surfacesYurasovskaya, Ekaterina 11 1900 (has links)
In his 1947 work "Theory of Braids" Emil Artin asked whether the braid
group remained unchanged when one considered classes of braids under linkhomotopy,
allowing each strand of a braid to pass through itself but not
through other strands. We generalize Artin's question to string links over
orientable surface M and show that under link-homotopy surface string links
form a group PBn(M), which is isomorphic to a quotient of the surface pure
braid group PBn(M). Surface braid groups and their properties are an area
of active research by González-Meneses, Paris and Rolfsen, Goçalves and
Guaschi, and our work explores the geometric and visual beauty of this
subject. We compute a presentation of PBn(M) in terms of the generators
and relations and discuss the orderability of the group in the case when the
surface in question is a unit disk D.
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Homotopy string links over surfacesYurasovskaya, Ekaterina 11 1900 (has links)
In his 1947 work "Theory of Braids" Emil Artin asked whether the braid
group remained unchanged when one considered classes of braids under linkhomotopy,
allowing each strand of a braid to pass through itself but not
through other strands. We generalize Artin's question to string links over
orientable surface M and show that under link-homotopy surface string links
form a group PBn(M), which is isomorphic to a quotient of the surface pure
braid group PBn(M). Surface braid groups and their properties are an area
of active research by González-Meneses, Paris and Rolfsen, Goçalves and
Guaschi, and our work explores the geometric and visual beauty of this
subject. We compute a presentation of PBn(M) in terms of the generators
and relations and discuss the orderability of the group in the case when the
surface in question is a unit disk D.
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Homotopy string links over surfacesYurasovskaya, Ekaterina 11 1900 (has links)
In his 1947 work "Theory of Braids" Emil Artin asked whether the braid
group remained unchanged when one considered classes of braids under linkhomotopy,
allowing each strand of a braid to pass through itself but not
through other strands. We generalize Artin's question to string links over
orientable surface M and show that under link-homotopy surface string links
form a group PBn(M), which is isomorphic to a quotient of the surface pure
braid group PBn(M). Surface braid groups and their properties are an area
of active research by González-Meneses, Paris and Rolfsen, Goçalves and
Guaschi, and our work explores the geometric and visual beauty of this
subject. We compute a presentation of PBn(M) in terms of the generators
and relations and discuss the orderability of the group in the case when the
surface in question is a unit disk D. / Science, Faculty of / Mathematics, Department of / Graduate
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Growth rate of 3-manifold homologies under branched coversCornish, James Stevens January 2018 (has links)
Over the last twenty years, a main focus of low-dimensional topology has been on categorified knot invariants such as knot homologies. This dissertation studies the case of two such homologies under the iteration of branched covering maps. In the first part, we find a spectral sequence on the sutured annular Khovanov homology of periodic links of period $r=2^i$. In the second part, we study the asymptotic growth rate of Heegaard Floer homology of cyclic branched covers of a knot as the branching number increases.
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Topological Symmetries of R^3January 2018 (has links)
acase@tulane.edu / 1 / Fang Sun
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The Hawaiian EarringBlack, Steven R. 26 November 1996 (has links)
Graduation date: 1997
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k-plane transforms and related integrals over lower dimensional manifoldsHenderson, Janet. January 1982 (has links)
No description available.
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Ribbon cobordisms:Huber, Marius January 2022 (has links)
Thesis advisor: Joshua E. Greene / We study ribbon cobordisms between 3-manifolds, i.e. rational homology cobordisms that admit a handle decomposition without 3-handles. We first define and study the more general notion of quasi-ribbon cobordisms, and analyze how lattice-theoretic methods may be used to obstruct the existence of a quasi-ribbon cobordism between two given 3-manifolds. Building on this and on previous work of Lisca, we then determine when there exists such a cobordism between two connected sums of lens spaces. In particular, we show that if an oriented rational homology sphere Y admitsa quasi-ribbon cobordism to a lens space, then Y must be homeomorphic to L(n, 1), up to orientation-reversal. As an application, we classify ribbon χ-concordances between connected sums of 2-bridge links. Lastly, we show that the notion of ribbon rational homology cobordisms yields a partial order on the set consisting of aspherical 3-manifolds and lens spaces, thus providing evidence towards a conjecture formulated by Daemi, Lidman, Vela-Vick and Wong. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.
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k-plane transforms and related integrals over lower dimensional manifoldsHenderson, Janet January 1982 (has links)
No description available.
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