Discrete Morse theory and extended \(L^2\) homology
In the first part of this interesting paper, the authors present a brief overview of the discrete Morse theory developed by \textit{R. Forman} [Conf. Proc. Lect. Notes Geom. Topol. 4, 112-125 (1995; Zbl 0867.57018); Topology 37, No. 5, 945-979 (1998; Zbl 0929.57020); Adv. Math. 134, No. 1, 90-145 (1998; Zbl 0896.57023)]. In the second part a Witten deformation technique is adapted by the authors to provide strong Morse inequalities for infinite CW complexes which have a finite cellular domain under the free cellular action of a discrete group. These inequalities are connected with those obtained by \textit{S. P. Novikov} and \textit{M. A. Shubin} [Sov. Math. Dokl. 34, 79-82 (1987); translation from Dokl. Akad. Nauk SSSR 289, 289-292 (1986; Zbl 0647.46049)] respectively by \textit{V. Mathai} and \textit{M. A. Shubin} [Russ. J. Math. Phys. 4, No. 4, 499-526 (1996; Zbl 0909.58048)].
scientific article; zbMATH DE number 1374982
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