SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS
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© 2019 The Author(s). We construct infinitely many compact, smooth 4-manifolds which are homotopy equivalent to S2 but do not admit a spine (that is, a piecewise linear embedding of S2 that realizes the homotopy equivalence). This is the remaining case in the existence problem for codimension-2 spines in simply connected manifolds. The obstruction comes from the Heegaard Floer d invariants.
Published Version (Please cite this version)10.1017/fms.2019.11
Publication InfoLevine, Adam; & Lidman, T (2019). SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS. Forum of Mathematics, Sigma, 7. 10.1017/fms.2019.11. Retrieved from https://hdl.handle.net/10161/18625.
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Assistant Professor of Mathematics
My research is in low-dimensional topology, the study of the shapes of 3- and 4-dimensional spaces (manifolds) and of curves and surfaces contained therein. Classifying smooth 4-dimensional manifolds, in particular, has been a deep challenge for topologists for many decades; unlike in higher dimensions, there is not enough "wiggle room" to turn topological problems into purely algebraic ones. Many of my projects reveal new complications in the topology of 4-manifolds, particularly related to emb