Strong Heegaard diagrams and strong L–spaces
Publication
, Journal Article
Greene, JE; Levine, AS
Published in: Algebraic and Geometric Topology
December 15, 2016
We study a class of 3–manifolds called strong L–spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. We provide evidence for the possibility that every strong L–space is the branched double cover of an alternating link in the three-sphere. For example, we establish this fact for a strong L–space admitting a strong Heegaard diagram of genus 2 via an explicit classification. We also show that there exist finitely many strong L–spaces with bounded order of first homology; for instance, through order eight, they are connected sums of lens spaces. The methods are topological and graph-theoretic. We discuss many related results and questions.
Duke Scholars
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Published In
Algebraic and Geometric Topology
DOI
EISSN
1472-2739
ISSN
1472-2747
Publication Date
December 15, 2016
Volume
16
Issue
6
Start / End Page
3167 / 3208
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Greene, J. E., & Levine, A. S. (2016). Strong Heegaard diagrams and strong L–spaces. Algebraic and Geometric Topology, 16(6), 3167–3208. https://doi.org/10.2140/agt.2016.16.3167
Greene, J. E., and A. S. Levine. “Strong Heegaard diagrams and strong L–spaces.” Algebraic and Geometric Topology 16, no. 6 (December 15, 2016): 3167–3208. https://doi.org/10.2140/agt.2016.16.3167.
Greene JE, Levine AS. Strong Heegaard diagrams and strong L–spaces. Algebraic and Geometric Topology. 2016 Dec 15;16(6):3167–208.
Greene, J. E., and A. S. Levine. “Strong Heegaard diagrams and strong L–spaces.” Algebraic and Geometric Topology, vol. 16, no. 6, Dec. 2016, pp. 3167–208. Scopus, doi:10.2140/agt.2016.16.3167.
Greene JE, Levine AS. Strong Heegaard diagrams and strong L–spaces. Algebraic and Geometric Topology. 2016 Dec 15;16(6):3167–3208.
Published In
Algebraic and Geometric Topology
DOI
EISSN
1472-2739
ISSN
1472-2747
Publication Date
December 15, 2016
Volume
16
Issue
6
Start / End Page
3167 / 3208
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics