Connected-sum decompositions of surfaces with minimally-intersecting filling pairs

Let Sg be a closed surface of genus g and let (α, β) be a filling pair on Sg; then i(α, β) ≥ 2g−1, where i is the (geometric) intersection number. Aougab and Huang demonstrated that (exponentially many) minimally-intersecting filling pairs exist on Sg when g > 2 by a construction which produces higher-genus surfaces with filling pairs as connected sums of lower-genus surfaces with filling pairs. We present a generalization of their construction which provides an explicit, algebraic means of determining the homeomorphism class of the resulting pair, and a criterion for determining when a surface with minimally-intersecting filling pair admits a decomposition as a connected sum.

Grantor dc:publisher

State University of New York at Buffalo

Year dc:date.issued

2018

Author dc:creator

• Nieland, Mark; 0000-0002-2830-2786

Contributors dc:contributor

• Menasco, William
• Mathematics

• mathematics

Statement dc:rights

• Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.
• Copyright retained by author.

Language dc:language

eng

Handle dc:identifier

http://hdl.handle.net/10477/77955

OAI record oai:identifier

https://ubir.buffalo.edu/oai/request?verb=GetRecord&metadataPrefix=qdc&identifier=oai%3Aubir.buffalo.edu%3A10477%2F77955