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2016 Invariants and structures of the homology cobordism group of homology cylinders
Minkyoung Song
Algebr. Geom. Topol. 16(2): 899-943 (2016). DOI: 10.2140/agt.2016.16.899

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 filtrations by subgroups by developing new homomorphisms. First, we define extended Milnor invariants by combining the ideas of Milnor’s link invariants and Johnson homomorphisms. They give rise to a descending filtration of the homology cobordism group of homology cylinders. We show that each successive quotient of the filtration is free abelian of finite rank. Second, we define 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 filtration is of infinite rank. Also we investigate further structures in the homology cobordism group of homology cylinders which previously known invariants do not detect.

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Minkyoung Song. "Invariants and structures of the homology cobordism group of homology cylinders." Algebr. Geom. Topol. 16 (2) 899 - 943, 2016. https://doi.org/10.2140/agt.2016.16.899

Information

Received: 30 December 2014; Revised: 20 April 2015; Accepted: 6 May 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1352.57024
MathSciNet: MR3493411
Digital Object Identifier: 10.2140/agt.2016.16.899

Subjects:
Primary: 57M27 , 57N10

Keywords: Hirzebruch-type invariant , Homology cobordism , homology cylinder , Milnor invariant

Rights: Copyright © 2016 Mathematical Sciences Publishers

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