Thesis (Ph.D.)--Michigan State University. Mathematics, 2008. / Title from PDF t.p. (viewed on July 24, 2009) Includes bibliographical references (p. 40-41). Also issued in print.

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains viii, 140 p.; also includes graphics. Includes bibliographical references (p. 139-140).

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 61-63). Available also in a digital version from Dissertation Abstracts.

Thesis (Doctoral)--Universität Bonn, 1990. / Includes bibliographical references.

Thesis--Bonn. / Extra t.p. with thesis statement inserted. Includes bibliographical references.

Thesis (doctoral)--Bonn, 1997. / Includes bibliographical references (p. 93-95).

Thesis (Ph.D.)--McMaster University, 2003. / Advisor: Ian Hambleton. Includes bibliographical references (leaves 109-112). Also available via World Wide Web.

Adviser: Peter B. Gilkey. ix, 128 leaves / A print copy of this title is available through the UO Libraries under the call number: MATH QA613 .Z43 2000 / Relative to a non-degenerate metric of signature (p, q), an algebraic curvature tensor is said to be IP if the associated skew-symmetric curvature operator R(π) has constant eigenvalues and if the kernel of R(π) has constant dimension on the Grassmanian of non-degenerate oriented 2-planes. A pseudo-Riemannian manifold with a non-degenerate indefinite metric of signature (p, q) is said to be IP if the curvature tensor of the Levi-Civita connection is IP at every point; the eigenvalues are permitted to vary with the point. In the Riemannian setting (p, q) = (0, m), the work of Gilkey, Leahy, and Sadofsky and the work of Ivanov and Petrova have classified the IP metrics and IP algebraic curvature tensors if the dimension is at least 4 and if the dimension is not 7. We use techniques from algebraic topology and from differential geometry to extend some of their results to the Lorentzian setting (p, q) = (1, m – 1) and to the setting of metrics of signature (p, q) = (2, m – 2).

This thesis explores connections between homotopy sheaves, manifold calculus of functors and operad theory. We argue that there is a deep overlap between these, and as evidence we give a new operadic description of the homotopy theoretical obstructions to deforming a smooth immersion into a smooth embedding. We then discuss an application which improves on some aspects of recent results of Arone-Turchin and Dwyer-Hess concerning spaces of long knots and high-dimensional variants. Along the way, we define fibrewise complete Segal spaces, a mild generalisation of Rezk's notion of complete Segal spaces. Also in the context of Segal spaces, we define right fibrations and prove a Grothendieck construction theorem for presheaves with values in spaces. Finally, we prove a result of independent interest which states that weakly k-reduced operads (those with contractible space of operations in arity j ? k) can be strictified when k = 0, 1.

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