Combinatorial Algebraic Topology

By Dmitry N. Kozlov. Algorithms and Computation in Mathematics, 2007

657 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8d03e9bccb5efb02fee168ab968c6cfa8884905c

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Spectra of combinatorial Laplace operators on simplicial complexes (2011, background): “The definition of i-path connectedness is different from the definition of i-connected simplicial complexes in [24].”
Gamma-positivity in combinatorics and geometry (2017, background): “Familiarity with basic notions on simplicial complexes and their geometric realizations is assumed; see [19, 73] [133, Lecture 1] for detailed expositions.”
Morse Theory for Filtrations and Efficient Computation of Persistent Homology (2013, methodology): “4 follows from the work of Forman [9] and has been re-proven in a variety of contexts [2,14,16,17].”
Colored Group Field Theory (2009, background): “1 in [31]) and not even a trisp (Definition 2.”
Topological Data Analysis (2012, background): “Moreover, if a simplex and all its faces have weak witnesses, the simplex also has a strong witness [ 21 ].”
Classifying Clustering Schemes (2010, background): “Functoriality has been a very useful framework for the discussion of various problems within mathematics over the last few decades; see [18, 21].”
Lost in translation: topological singularities in group field theory (2010, background): “alization to open graphs [39] being immediate. 4 2 SimplicialPseudoManifolds In this section we review some deﬁnitions and properties of normal simplicial pseudo manifolds (following the notations of [43]) relevant to our subsequent analysis of GFT’s. A ﬁnite abstract simplicial complex4 is a ﬁnite ”
Two’s company, three (or more) is a simplex (2016, methodology): “atrix that can be subsequently interrogated mathematically. This is by no means an exhaustive list of complexes of potential interest to the neuroscience community; for further examples, we recommend [34, 40]. How do we measure the structure of simplicial complexes? Just as with network models, once”
Higher topological complexity and its symmetrization (2010, background): “theory of open manifolds, and seems likely to have interesting new applications. Our proposal ﬁts well with an active ongoing mutual feedback between topology and combinatorics—of which Kozlov’s book [Ko08] is a good example. One of the most fundamental properties on which this relationship rests is”