46 III Complexes III.1 **Simplicial** Complexes There are many ways to represent atopological space, one beingacollection of simplices that are glued to each other inastructured manner.

Using Quadratic **Simplicial** Elements for Hierarchical Approximation and Visualization David F. Wiley a, Henry R. Childs b, Bernd Hamann a, Kenneth I. Joy a, and Nelson L. Max a, c a Center for Image Processing and Integrated Computing (CI PIC) , Department of Computer Science, University of CA ...

PCMI Undergraduate Faculty Program 2004 Participant Projects Homology of **Simplicial** Complexes Darrell Allgaier (Grove City College), David Perkinson (Reed College), Sarah AnnStewart (North Central College), John Thurber (Eastern Oregon University) Abstract This is an introduction to the homology ...

Discrete Morse Theory on **Simplicial** Complexes August 27,2009 ALEXZORN ABSTRACT: Following [2]and[3], we introducea combinatorial analog of topological Morse theory, and show how the introduction of a discrete Morse function on a **simplicial** complex gives rise to a discrete vector eld.

Although the **Simplicial** Approximation Theorem gives a **simplicial** approximation to every continuous map (between nite polyhedra), nowhere does it say that a **simplicial** approximation to a retraction is, or can be chosen to be, a **simplicial** retraction.

FINITE SPACES AND **SIMPLICIAL** COMPLEXES NOTES FOR REU BYJ.P. MAY 1. Statements of results Finite **simplicial** complexes provide a general class of spaces that is sufficient for most purposes of basic algebraic topology.

Abstract In this paper, we study the combinatorial Laplacian operator on the vector space of oriented chains over Rofafinite **simplicial** complex.

2 VIN DE SILVA The PLEXsoftware was written with the following task in mind: to recover the Bettinumbers of the space X, when Xis assumed to be homeomorphic toa finite **simplicial** complex.

This article is ab out generalizing the Matrix-Tree Theorem from graphs to **simplicial** complexes.

**Simplicial** Dijkstra and A*Algorithms for Optimal Feedback Planning DmitryS. Yershovand Steven M. LaValle Abstractâ€”This paper considers the Euclidean shortest path problem among obstacles in R n.