Correction terms, Z_2-Thurston norm, and triangulations
We explicitly construct layered-triangulations for manifolds admitting a genus-one open book decomposition with connected binding. This construction gives an upper bound to the complexity of these manifolds. In a different direction, we show that the correction terms in Heegaard Floer homology give a lower bound to the genus of one-sided Heegaard splittings and the Z_2-Thurston norm. Using a result of Jaco–Rubinstein–Tillmann, this gives a lower bound to the complexity of certain closed 3-manifolds. We illustrate our theorems with some examples.
© 2015 Elsevier B.V. Received 5 December 2014; Received in revised form 1 September 2015; Accepted 2 September 2015; Available online 15 September 2015. We wish to thank Ian Agol, Danny Ruberman and Hyam Rubinstein for conversations which motivated this work. The first author was partially supported by NSF grant numbers DMS-1103976, DMS-1252992, and an Alfred P. Sloan Research Fellowship. The second author was partially supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (RGC Project No. CUHK24300714).
Submitted - 1410.5342v1.pdf