Abstract
In this chapter we define the concept of a cellular resolution, which lays the ground for the application of discrete Morse theory in Commutative Algebra. Since the concept of a cellular resolution uses the concept of multigraded free resolutions and CW-complexes as an ingredient we define these concepts first. Indeed we have already given definitions of resolutions and simplicial complexes in Chapter 1 in a more informal way. In this chapter will be more rigorous and also add more details and examples. More precisely, Sections 2.1 - 2.4 give the definitions of free resolutions, CW-complexes, simplicial complexes, cellular free resolutions, monomial modules and co-Artinian monomial modules.
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© 2007 Springer
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Orlik, P., Welker, V. (2007). Basic De.nitions and Examples. In: Fløystad, G. (eds) Algebraic Combinatorics. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68376-6_5
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DOI: https://doi.org/10.1007/978-3-540-68376-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68375-9
Online ISBN: 978-3-540-68376-6
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