TY - JOUR
T1 - Simplified broken Lefschetz fibrations and trisections of 4-manifolds
AU - Baykur, R. Inanç
AU - Saeki, Osamu
N1 - Funding Information:
ACKNOWLEDGMENTS. We thank Kenta Hayano for his careful comments on a draft of this manuscript. This work was partially supported by NSF Grant DMS-1510395 (to R.I.B.) and Japan Society for the Promotion of Science KAKENHI Grants JP23244008, JP23654028, JP15K13438, JP16K13754, JP16H03936, JP17H01090, and JP17H06128 (to O.S.).
Funding Information:
We thank Kenta Hayano for his careful comments on a draft of this manuscript. This work was partially supported by NSF Grant DMS-1510395 (to R.I.B.) and Japan Society for the Promotion of Science KAKENHI Grants JP23244008, JP23654028, JP15K13438, JP16K13754, JP16H03936, JP17H01090, and JP17H06128 (to O.S.).
Publisher Copyright:
© 2018 National Academy of Sciences. All rights reserved.
PY - 2018/10/23
Y1 - 2018/10/23
N2 - Shapes of 4D spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, to derive simple decompositions into much betterunderstood manifold pieces. Our methods not only allow us to produce various interesting families of examples but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.
AB - Shapes of 4D spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, to derive simple decompositions into much betterunderstood manifold pieces. Our methods not only allow us to produce various interesting families of examples but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.
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U2 - 10.1073/pnas.1717175115
DO - 10.1073/pnas.1717175115
M3 - Article
C2 - 30348799
AN - SCOPUS:85055438841
SN - 0027-8424
VL - 115
SP - 10894
EP - 10900
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 43
ER -