NDLI: Computational homotopy of finite regular CW-spaces

Content Provider	Springer Nature Link
Author	Ellis, Graham Hegarty, Fintan
Copyright Year	2013
Abstract	We describe a computational approach to the basic homotopy theory of finite regular CW-spaces, paying particular attention to spaces arising as a union of closures of $$n$$ -cells with isomorphic face posets. Deformation retraction methods for computing fundamental groups, integral homology and persistent homology are given in this context. The approach is not new but our account contains some new features: (i) certain computational advantages of a permutahedral face poset are identified and utilized; (ii) the notion of lattice complex is introduced as a data type for implementing a general class of regular CW-spaces (including certain pure cubical and pure permutahedral subspaces of flat manifolds such as $$\mathbb{R }^n$$ ); (iii) zig-zag homotopy retractions are introduced as an initial procedure for reducing the number of cells of low-dimensional lattice spaces; more standard discrete vector field techniques are applied for further cellular reduction; (iv) a persistent homology approach to feature recognition in low-dimensional digital images is illustrated; (v) fundamental groups are computed; (vi) algorithms are implemented in the gap system for computational algebra, allowing for their output to benefit from the system’s vast library of efficient algebraic procedures.
Starting Page	25
Ending Page	54
Page Count	30
File Format	PDF
ISSN	21938407
Journal	Journal of Homotopy and Related Structures
Volume Number	9
Issue Number	1
e-ISSN	15122891
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-05-07
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Algebra Functional Analysis Algebraic Topology Persistent Betti numbers Number Theory Fundamental group Integral homology Computational topology
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Geometry and Topology

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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