Invariants and Structures of the Homology Cobordism Group of Homology Cylinders
- Title
- Invariants and Structures of the Homology Cobordism Group of Homology Cylinders
- Authors
- 송민경
- Date Issued
- 2015
- Publisher
- 포항공과대학교
- Abstract
- The homology cobordism group of homology cylinders is a generalization of the
mapping class group and the string link concordance group. We study this group
and its ltrations by subgroups by developing new homomorphisms. First, we de ne
extended Milnor invariants by combining the ideas of Milnor's link invariants and
Johnson homomorphisms. They give rise to a descending ltration of the homology
cobordism group of homology cylinders.We show that each successive quotient of the
ltration is free abelian of nite rank. Second, we de ne Hirzebruch-type intersection
form defect invariants obtained from iterated p-covers for homology cylinders. Using
them, we show that the abelianization of the intersection of our ltration is of in nite
rank. Also we investigate further structures in the homology cobordism group of
homology cylinders which previously known invariants do not detect.
- URI
- http://postech.dcollection.net/jsp/common/DcLoOrgPer.jsp?sItemId=000002069628
https://oasis.postech.ac.kr/handle/2014.oak/92927
- Article Type
- Thesis
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