On Regular Genus and G-Degree of PL 4-Manifolds With Boundary
Authors
-
Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016 ,IN
Biplab Basak -
Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016 ,INManisha Binjola
DOI:
https://doi.org/10.18311/jims/2024/30716Keywords:
PL-manifolds, Crystallizations, Regular genus, Gurau degree (G-degree)Abstract
In this article, we introduce two novel PL-invariants: weighted regular genus and weighted G-degree for manifolds with boundaries. We establish that for any PL 4-manifoldM with non-spherical boundary components, the regular genus G(M) of M is at least the weighted regular genus Ḡ(M). Additionally, another inequality asserts that the weighted G-degree -˜DG(M) of M is always greater than or equal to the G-degree DG(M) of M.
Furthermore, we derive lower bounds for the weighted regular genus ˜Ḡ (M) and weighted G-degree ˜DG(M) for a PL 4-manifold with nonspherical boundary components. This contributes to an enhancement of the existing lower bounds for the regular genus G(M) of the manifold. Subsequently, we define two classes of gems for a PL 4-manifold M with boundary: one comprised of semi-simple gems and the other consisting of weak semi-simple gems. We prove that the lower bounds for the weighted G-degree and weighted regular genus are achieved within these two classes, respectively.
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Copyright (c) 2024 Biplab Basak, Manisha Binjola
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2022-12-02
Published 2024-01-01
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