In a former life Allen Fogelsanger completed a dissertation in mathematics for which Cornell University awarded him a Ph.D. in 1988. It is made available here as penance for having never published it.

For slow internet connections the dissertation has been divided into pdf documents as follows:

All Rights Reserved

- Preliminaries: title page, copyright page, abstract, biographical sketch, acknowledgements, table of contents, list of figures (8 pages, 769kb)
- Chapter 1: Introduction (pp. 1-16, 1.98mb)
- Chapter 2: Basic Definitions (pp. 17-29, 2.00mb)
- Chapter 3: The Decomposition of a Minimal p-Cycle Complex (pp. 30-36, 1014kb)
- Chapters 4-7: Proofs (pp. 37-52, 2.25mb)
- Chapter 8: Some Applications; and List of References (pp. 53-60, 1.23mb)

The pages were scanned at 600 dpi and converted into pdf using ABBYY FineReader 6.0 Sprint. They are imperfectly searchable for words without symbols.

For further reading see:

- E. Kann,
Infinitesimal rigidity of almost-convex oriented polyhedra of arbitrary Euler characteristic

*Pacific Journal of Mathematics*144/1 (Jul 1990): 71-103 - B. Hendrickson,
Conditions for unique graph realizations

*SIAM Journal on Computing*21/1 (Feb 1992): 65-84 - I. Sabitov,
On an algorithm for polyhedron bendability test

*Vestnik Moskovskogo Universiteta Seriya 1 Matematika Mekhanika*2 (Mar-Apr 1994): 56-61 - W. Whiteley,
How to describe or design a polyhedron

*Journal of Intelligent and Robotic Systems*11/1-2 (1994): 135-160 - T.-S. Tay,
Lower-bound theorems for pseudomanifolds

*Discrete and Computational Geometry*13/2 (Mar 1995): 203-216 - T.-S. Tay, N. White, and W. Whitelay,
Skeletal rigidity of simplicial complexes 1

*European Journal of Combinatorics*16/4 (Jul 1995): 381-403 - T.-S. Tay, N. White, and W. Whitelay,
Skeletal rigidity of simplicial complexes 2

*European Journal of Combinatorics*16/5 (Sep 1995): 503-523 - T.-S. Tay and W. Whiteley,
A homological interpretation of skeletal rigidity

*Advances in Applied Mathematics*25/1 (Jul 2000): 102-151 - I. Sabitov,
The solution of polyhedra,

*Doklady Mathematics*63/2 (Mar-Apr 2001): 170-173 - R. Erdahl, K. Rybnikov, and S. Ryshkov,
On traces of d-stresses in the skeletons of lower dimensions of piecewise-linear d-manifolds,

*European Journal of Combinatorics*22/6 (Aug 2001): 801-820 - E. Nevo,
Rigidity and the lower bound theorem for doubly Cohen-Macaulay complexes,

*Discrete and Computational Geometry*39/1-3 (Mar 2008): 411-418 - I. Novik and E. Swartz,
Applications of Klee's Dehn-Sommerville relations,

*Discrete and Computational Geometry*42/2 (Sep 2009): 261-276 - I. Sabitov,
Algebraic methods for solution of polyhedra,

*Russian Mathematical Surveys*66/3 (2011): 445-505 - M. Goff, S. Klee and I. Novik,
Balanced complexes and complexes without large missing faces,

*Arkiv for Matematik*49/2 (Oct 2011): 335-350

This webpage was last revised on August 4, 2012.

Allen Fogelsanger

608 5th St., Apt. 4R

Brooklyn, New York 11215-3573

E-mail: allen[dot]fogelsanger[at]gmail[dot]com