Open Research Oklahoma
ORO serves as the home for Oklahoma State University's open-access intellectual output. It includes digital dissertations, faculty publications, OSU Extension publications, undergraduate research, open educational resources, and more. Email openresearch@okstate.edu to see how your Oklahoma-based institution can join.
Recent Submissions
Publication Homology 3-spheres which admit no pl involutions(Mathematical Sciences Publishers, 1981-06)An infinite family of irreducible homology 3-spheres is constructed, each member of which admits no PL involutions. © 1981, University of California, Berkeley. All Rights Reserved.Publication R²-irreducible universal covering spaces of P²-irreducible open 3-manifolds(Mathematical Sciences Publishers, 1998)An irreducible open 3-manifold W is R²-irreducible if it contains no non-trivial planes, i.e. given any proper embedded plane in W some component of W −II must have closure an embedded halfspace R² ×(0, ∞). In this paper it is shown that if M is a connected, P²-irreducible, open 3-manifold such that π₁(M) is finitely generated and the universal covering space M of M is R²-irreducible, then either M̃ is homeomorphic to R³ or π₁(M) is a free product of infinite cyclic groups and fundamental groups of closed, connected surfaces other than S² or P². Given any finitely generated group G of this form, uncountably many P²-irreducible, open 3-manifolds M are constructed with π₁(M) ≅ G such that the universal covering space M is R²-irreducible and not homeomorphic to R³; the M are pairwise non-homeomorphic. Relations are established between these results and the conjecture that the universal covering space of any irreducible, orientable, closed 3-manifold with infinite fundamental group must be homeomorphic to R³.Publication Concordance of Seifert surfaces(Mathematical Sciences Publishers, 2019-02)We prove that every oriented nondisk Seifert surface F for an oriented knot K in S³ is smoothly concordant to a Seifert surface F′ for a hyperbolic knot K′ of arbitrarily large volume. This gives a new and simpler proof of the result of Friedl and of Kawauchi that every knot is S-equivalent to a hyperbolic knot of arbitrarily large volume. The construction also gives a new and simpler proof of the result of Silver and Whitten and of Kawauchi that for every knot K there is a hyperbolic knot K′ of arbitrarily large volume and a map of pairs f :(S³, K′)→(S³, K) which induces an epimorphism on the knot groups. An example is given which shows that knot Floer homology is not an invariant of Seifert surface concordance. We also prove that a set of finite volume hyperbolic 3-manifolds with unbounded Haken numbers has unbounded volumes.Publication On covering translations and homeotopy groups of contractible open n-manifolds(American Mathematical Society (AMS), 1999-10-06)This paper gives a new proof of a result of Geoghegan and Mihalik which states that whenever a contractible open n-manifold W which is not homeomorphic to Rⁿ is a covering space of an n-manifold M and either n ≥ 4 or n = 3 and W is irreducible, then the group of covering translations injects into the homeotopy group of W. ©2000 American Mathematical Society.Publication Simple knots in compact, orientable 3-manifolds(American Mathematical Society (AMS), 1982-09)A simple closed curve J in the interior of a compact, orientable 3-manifold M is called a simple knot if the closure of the complement of a regular neighborhood of J in M is irreducible and boundary-irreducible and contains no non-boundary-parallel, properly embedded, incompressible annuli or tori. In this paper it is shown that every compact, orientable 3-manifold M such that ∂M contains no 2-spheres contains a simple knot (and thus, from work of Thurston, a knot whose complement is hyperbolic). This result is used to prove that such a 3-manifold is completely determined by its set K(M) of knot groups, i.e, the set of groups π₁, (M - J) as J ranges over all the simple closed curves in M. In addition, it is proven that a closed 3-manifold M is homeomorphic to S³ if and only if every simple closed curve in M shrinks to a point inside a connected sum of graph manifolds and 3-cells. © 1982 American Mathematical Society.
Communities in Open Research Oklahoma
Select a community to browse its collections.