2018/03/29 by Dominik Wrazidlo, Wrazidlo, Dominik · 1 citation
Computer Science · Mathematics · #57R45 #57R60 #57R65 (Secondary) #57R90 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1803.11177
openalex publication_date 2018/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We call a Morse function f on a closed manifold k-constrained if neither f nor -f has critical points of indefinite Morse index < k. In this paper we study bordism groups of k-constrained Morse functions, and thus interpolate between the case k = 1 of bordism groups of Morse functions (computed by Ikegami) and the case k ≫ 1 of bordism groups of special generic functions (computed by Saeki). We employ Levine's elimination of cusps, Stein factorization, the two-index theorem of Hatcher-Wagoner, and a handle extension theorem for fold maps due to Gay-Kirby to show that the notion constrained bordism is strongly related to so-called connective bordism. As an application of our results we show that the oriented bordism group of constrained Morse functions detects exotic Kervaire spheres in certain dimensions.