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Computing the homology of groups: the geometric way
homology of groups the geometric way Algebraic Topology
2011/9/14
Abstract: In this paper we present several algorithms related with the computation of the homology of groups, from a geometric perspective (that is to say, carrying out the calculations by means of si...
Computing the crosscap number of a knot using integer programming and normal surfaces
integer programming normal surfaces crosscap number of a knot Geometric Topology
2011/9/5
Abstract: The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers a...
Stochastic Homology. Reduction Formulas for Computing Stochastic Betti Numbers of Maximal Random Complexes with Discrete Probabilities. Computation and Applications
Stochastic Homology Stochastic Betti Numbers Maximal Random Complexes Algebraic Topology
2011/8/25
Abstract: Given a chain complex with the only modi?cation that each cell of the complex has a probability distribution assigned. We will call this complex - a random complex and what should be underst...
Defining and Computing Topological Persistence for 1-cocycles
Topological Persistence 1-cocycles
2011/2/22
The concept of topological persistence, introduced recently in computational topology, finds applications in studying a map in relation to the topology of its domain. Since its introduction, it has be...