Algebraic <em>k</em>-theory of orbispaces Maxine Elena Calle

Format:

Book

Thesis/Dissertation

Author/Creator:

Calle, Maxine Elena, author.

Contributor:

University of Pennsylvania. Mathematics., degree granting institution.

Language:

English

Subjects (All):

Mathematics.

Theoretical mathematics.

0405.

0642.

Local Subjects:

Mathematics.

Theoretical mathematics.

0405.

0642.

Genre:

Academic theses

Physical Description:

1 online resource (186 pages)

Contained In:

Dissertations Abstracts International 87-12B

Place of Publication:

Ann Arbor : ProQuest Dissertations and Theses, 2026

Language Note:

English

Summary:

This thesis develops a refinement of Waldhausen's higher algebraic K-theory of spaces to the setting of orbifolds, and more generally orbispaces, which generalize smooth manifolds by allowing for certain kinds of singularities. We are motivated by the classical connection between Waldhausen's K-theory construction and manifold topology, particularly in regard to h-cobordisms, and we expect our constructions to have rich geometric applications to orbifolds in analogy with the smooth setting.The central objects of study are orbispaces and their stable counterparts, orbispectra. We construct K-theory functors that produce orbispectra from categorical data. In particular, we associate to every orbispace X an orbispectrum A(X) which refines Waldhausen's original construction. This orbispectrum is closely related to the genuine equivariant algebraic K-theory construction of Malkiewich-Merling, and consequently encodes G-equivariant analogues of classical invariants such as the Euler characteristic and the Wall finiteness obstruction for all finite groups G. We show that these equivariant invariants extend to intrinsic invariants of orbispaces, realized in the homotopy groups of a complementary spectrum AO(X), defined as the K-theory of the category of retractive orbispaces over X.In the course of our work, we develop a model for orbispectra as spectral Mackey functors. A consequence of this identification is that the homotopy groups of an orbispectrum naturally assemble into globally-defined Mackey functors in the sense of Bouc and Webb, providing a uniform algebraic framework for these invariants. As a further application, we develop a general theory of Bredon cohomology for orbispaces and show that such cohomology theories are representable by Eilenberg-Maclane orbispectra

Notes:

Source: Dissertations Abstracts International, Volume: 87-12, Section: B.

Advisors: Merling, Mona Committee members: Gadish, Nir; Fernandez Herrero, Andres

Ph.D. University of Pennsylvania 2026

Vendor supplied data

Local Notes:

School code: 0175

ISBN:

9798247980094

Access Restriction:

Restricted for use by site license