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Pseudo-trisections of four-manifolds with boundary

Published online by Cambridge University Press:  11 February 2025

Shintaro Fushida-Hardy Open the ORCID record for Shintaro Fushida-Hardy [Opens in a new window]
Shintaro Fushida-Hardy*
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA, United States URL: https://sfushidahardy.github.io
*
e-mail: [email protected]
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Abstract

We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove existence and uniqueness of pseudo-trisections, and further establish a one-to-one correspondence between pseudo-trisections and their diagrammatic representations. We next introduce the concept of pseudo-bridge trisections of neatly embedded surfaces in smooth oriented compact 4-manifolds. We develop a diagrammatic theory of pseudo-bridge trisections and provide examples of computations of invariants of neatly embedded surfaces in 4-manifolds using said diagrams.

Keywords

Trisectiontrisection diagramfour-manifoldmanifold with boundary
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 47
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This work was supported in part by the NSF grant DMS-2003488.

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