The cobordism group of homology cylinders

DOI10.1112/S0010437X10004975zbMath1225.57003arXiv0909.5580OpenAlexW3100360537MaRDI QIDQ3008420

Stefan Friedl, Taehee Kim, Jae Choon Cha

Publication date: 15 June 2011

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.5580

zbMATH Keywords

mapping class grouporientedconnected and compact surface of genus \(g\) with \(n\) boundary componentsgroup of homology cobordism classes of homology cylinders

Mathematics Subject Classification ID

Related Items (10)

A non-commutative Reidemeister-Turaev torsion of homology cylinders ⋮ Abelian quotients of monoids of homology cylinders ⋮ Morita’s trace maps on the group of homology cobordisms ⋮ Exponential growth of torsion in abelian coverings ⋮ Homology cylinders of higher-order ⋮ Characteristic classes of moduli spaces— Riemann surface, graph, homology cobordism ⋮ Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras ⋮ An extension of the LMO functor ⋮ FACTORIZATION FORMULAS AND COMPUTATIONS OF HIGHER-ORDER ALEXANDER INVARIANTS FOR HOMOLOGICALLY FIBERED KNOTS ⋮ Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces

Cites Work

• Mahler measure, links and homology growth
• Homology cobordism group of homology 3-spheres
• The topology of four-dimensional manifolds
• The structure of the Torelli group. I: A finite set of generators for \({\mathcal I}\)
• The Magnus representation and higher-order Alexander invariants for homology cobordisms of surfaces
• The structure of the Torelli group. III: The abelianization of \({\mathcal S}\)
• The genus 2 Torelli group is not finitely generated
• A duality theorem for Reidemeister torsion
• The Torelli groups for genus 2 and 3 surfaces
• Some finitely presented subgroups of the automorphism group of a free group
• Twisted Alexander invariants, Reidemeister torsion, and Casson-Gordon invariants
• Claspers and finite type invariants of links
• Knot Floer homology detects fibred knots
• Homology and central series of groups
• Knot cobordism groups in codimension two
• Invariants of knot cobordism
• THE GASSNER REPRESENTATION FOR STRING LINKS
• A survey of the Torelli group
• Instanton Homology of Seifert Fibred Homology Three Spheres
• Reidemeister torsion in knot theory
• Finite type invariants and n-equivalence of 3-manifolds
• Mahler Measure of Alexander Polynomials
• Whitehead torsion
• Homology cylinders: an enlargement of the mapping class group
• Reidemeister-Turaev torsion of 3-dimensional Euler structures with simple boundary tangency and pseudo-Legendrian knots

This page was built for publication: The cobordism group of homology cylinders