Abstract
Whitehead’s theory of simple homotopy types is inspired by Tietze’s theorem in combinatorial group theory, which states that any finite presentation of a group could be deformed into any other by a finite sequence of elementary moves, which are now called Tietze transformations. Whitehead translated these algebraic moves into the well-known geometric moves of elementary collapses and expansions of finite simplicial complexes.
Keywords
- Simplicial Complex
- Weak Point
- Mapping Cylinder
- Barycentric Subdivision
- Whitehead Group
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© 2011 Springer-Verlag Berlin Heidelberg
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Barmak, J.A. (2011). Simple Homotopy Types and Finite Spaces. In: Algebraic Topology of Finite Topological Spaces and Applications. Lecture Notes in Mathematics(), vol 2032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22003-6_4
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DOI: https://doi.org/10.1007/978-3-642-22003-6_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22002-9
Online ISBN: 978-3-642-22003-6
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