CS 85/185
Spring 2007
Introduction to
Computational
Topology
Announcements
Administrivia
Schedule
Resources
Resources
References for Mathematical Terms & Concepts
MathWorld
PlanetMath
Wikipedia
Course Notes
6. Homology
5. Homotopy
4. Group Theory
3. Simplicial Complexes
2. Surface Topology
1. Point Set Topology
0. Introduction
Homeworks
Homework Four
Homework Three
Homework Two
Homework One
Supplementary Handouts
Coordinate-free coverage in sensor networks with controlled boundaries via homology
–
Vin de Silva
and
Robert Ghrist
Homological Sensor Networks
–
Vin de Silva
and
Robert Ghrist
Splitting (complicated) surfaces is hard
–
Erin Chambers
,
Éric Colin de Verdière
,
Jeff Erickson
,
Francis Lazarus
, and
Kim Whittlesey
Greedy optimal homotopy and homology generators
–
Jeff Erickson
and
Kim Whittlesey
Computing Persistent Homology
–
Afra Zomorodian
and
Gunnar Carlsson
Barcodes
–
Robert Ghrist
Witness complex
–
Vin de Silva
and
Gunnar Carlsson
Quad-Edge (with Code)
–
Dani Lischinski
Edge-Facet
– from Ernst Mücke's thesis
Poincaré Conjecture
–
John Milnor
Topo the World
–
Jean-Pierre Petit
and John Murphy
The Poincaré Conjecture Proved
.
Science Magazine
, April 26, 2007.
Collins, G. P. The Shapes of Space.
Scientific American
, 291(1), 2004. (Hardcopy)
Thurston, W. P. and Weeks, J. R. The Mathematics of Three-dimensional Manifolds.
Scientific American
, 251(1) (1984). (Hardcopy)
Markov's Proof
– A. A. Markov
Max's Eversion
–
Nelson Max
and William H. Clifford, Jr.
Conway's ZIP
–
George Francis
and
Jeff Weeks
Software
CHomP
PLEX
RoffView
Computer Science
Dartmouth College