Volume 12, issue 3 (2012)

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Homology cylinders of higher-order

Takahiro Kitayama

Algebraic & Geometric Topology 12 (2012) 1585–1605
Bibliography
1 H Bass, A Heller, R G Swan, The Whitehead group of a polynomial extension, Inst. Hautes Études Sci. Publ. Math. (1964) 61 MR0174605
2 J Cha, S Friedl, Twisted torsion invariants and link concordance, to appear in Forum Math. arXiv:1001.0926
3 J C Cha, S Friedl, T Kim, The cobordism group of homology cylinders, Compos. Math. 147 (2011) 914 MR2801405
4 T D Cochran, Noncommutative knot theory, Algebr. Geom. Topol. 4 (2004) 347 MR2077670
5 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. 157 (2003) 433 MR1973052
6 J Conant, P Teichner, Grope cobordism of classical knots, Topology 43 (2004) 119 MR2030589
7 R Fintushel, R J Stern, Instanton homology of Seifert fibred homology three spheres, Proc. London Math. Soc. 61 (1990) 109 MR1051101
8 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
9 S Friedl, Reidemeister torsion, the Thurston norm and Harvey's invariants, Pacific J. Math. 230 (2007) 271 MR2309160
10 M Furuta, Homology cobordism group of homology 3–spheres, Invent. Math. 100 (1990) 339 MR1047138
11 S Garoufalidis, J Levine, Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphism, from: "Graphs and patterns in mathematics and theoretical physics", Proc. Sympos. Pure Math. 73, Amer. Math. Soc. (2005) 173 MR2131016
12 H Goda, T Sakasai, Homology cylinders in knot theory arXiv:0807.4034
13 H Goda, T Sakasai, Abelian quotients of monoids of homology cylinders, Geom. Dedicata 151 (2011) 387 MR2780758
14 M Goussarov, Finite type invariants and $n$–equivalence of 3–manifolds, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 517 MR1715131
15 K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
16 K Habiro, G Massuyeau, From mapping class groups to monoids of homology cobordisms: a survey, to appear in Handbook of Teichmüller theory III
17 S L Harvey, Higher-order polynomial invariants of 3–manifolds giving lower bounds for the Thurston norm, Topology 44 (2005) 895 MR2153977
18 D L Johnson, Homeomorphisms of a surface which act trivially on homology, Proc. Amer. Math. Soc. 75 (1979) 119 MR529227
19 P Kirk, C Livingston, Twisted Alexander invariants, Reidemeister torsion, and Casson–Gordon invariants, Topology 38 (1999) 635 MR1670420
20 J Levine, Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243 MR1823501
21 J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358 MR0196736
22 S Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J. 70 (1993) 699 MR1224104
23 S Morita, Symplectic automorphism groups of nilpotent quotients of fundamental groups of surfaces, from: "Groups of diffeomorphisms", Adv. Stud. Pure Math. 52, Math. Soc. Japan (2008) 443 MR2509720
24 R B Mura, A Rhemtulla, Orderable groups, Lecture Notes in Pure and Applied Mathematics 27, Marcel Dekker (1977) MR0491396
25 D S Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons] (1977) MR470211
26 J Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978) 347 MR0494115
27 A H Rhemtulla, Residually $F_{p}$–groups, for many primes $p$, are orderable, Proc. Amer. Math. Soc. 41 (1973) 31 MR0332615
28 T Sakasai, A survey of Magnus representations for mapping class groups and homology cobordisms of surfaces, to appear in Handbook of Teichmüller theory III
29 T Sakasai, Higher-order Alexander invariants for homology cobordisms of a surface, from: "Intelligence of low dimensional topology 2006", Ser. Knots Everything 40, World Sci. Publ., Hackensack, NJ (2007) 271 MR2371735
30 T Sakasai, The Magnus representation and higher-order Alexander invariants for homology cobordisms of surfaces, Algebr. Geom. Topol. 8 (2008) 803 MR2443097
31 V Turaev, A homological estimate for the Thurston norm arXiv:math/0207267
32 V Turaev, Introduction to combinatorial torsions, Lectures in Mathematics ETH Zürich, Birkhäuser (2001) MR1809561