Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus 2

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Christian Hatamian
Alexandr Prishlyak
https://orcid.org/0000-0002-7164-807X

Abstract


The present paper investigates Heegaard diagrams of non-orientable closed 3-manifolds, i.e. a non-orienable closed surface together with two sets of meridian disks of both handlebodies.
It is found all possible non-orientable genus 2 Heegaard diagrams of complexity less than 6.
Topological properties of Morse flows on closed smooth non-orientable 3-manifolds are described.
Normalized Heegaard diagrams are furhter used for classification Morse flows with a minimal number of singular points and singular trajectories

 



 

Keywords:
topological equivalence, Heegaard diagram, Morse flow

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How to Cite
Hatamian, C., & Prishlyak, A. (2020). Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus 2. Proceedings of the International Geometry Center, 13(3), 33-48. https://doi.org/10.15673/tmgc.v13i3.1779
Section
Papers
Author Biographies

Christian Hatamian, Institute of Mathematics NAS of Ukraine

Institute of Mathematics NAS of Ukraine, 3, Str. Tereschenkivska, Kyiv, 01024 Ukraine

Alexandr Prishlyak, Taras Shevchenko National University of Kyiv

Taras Shevchenko National University of Kyiv, 64/13, Str. Volodymyrska, Kyiv, Ukraine