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:

The Generic Rigidity of Minimal Cycles

by Allen Fogelsanger

© Allen Fogelsanger 1988
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