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26. CMB 2011 (vol 54 pp. 283)

Hillman, J. A.; Roushon, S. K.
 Surgery on $\widetilde{\mathbb{SL}} \times \mathbb{E}^n$-Manifolds We show that closed $\widetilde{\mathbb{SL}} \times \mathbb{E}^n$-manifolds are topologically rigid if $n\geq 2$, and are rigid up to $s$-cobordism, if $n=1$. Keywords:topological rigidity, geometric structure, surgery groups Categories:57R67, 57N16

27. CMB 2010 (vol 54 pp. 556)

Teragaito, Masakazu
 Cyclic Surgery Between Toroidal Surgeries We show that there is an infinite family of hyperbolic knots such that each knot admits a cyclic surgery $m$ whose adjacent surgeries $m-1$ and $m+1$ are toroidal. This gives an affirmative answer to a question asked by Boyer and Zhang. Keywords:cyclic surgery, toroidal surgeryCategory:57M25

28. CMB 2010 (vol 54 pp. 147)

Nelson, Sam
 Generalized Quandle Polynomials We define a family of generalizations of the two-variable quandle polynomial. These polynomial invariants generalize in a natural way to eight-variable polynomial invariants of finite biquandles. We use these polynomials to define a family of link invariants that further generalize the quandle counting invariant. Keywords:finite quandles, finite biquandles, link invariantsCategories:57M27, 76D99

29. CMB 2010 (vol 53 pp. 706)

Roberts, R.; Shareshian, J.
 Non-Right-Orderable 3-Manifold Groups We exhibit infinitely many hyperbolic $3$-manifold groups that are not right-orderable. Categories:20F60, 57M05, 57M50

30. CMB 2010 (vol 53 pp. 542)

Pintea, Cornel
 Smooth Mappings with Higher Dimensional Critical Sets In this paper we provide lower bounds for the dimension of various critical sets, and we point out some differential maps with high dimensional critical sets. Categories:58K05, 57R70

31. CMB 2009 (vol 52 pp. 257)

Ikeda, Toru
 Essential Surfaces in Graph Link Exteriors An irreducible graph manifold $M$ contains an essential torus if it is not a special Seifert manifold. Whether $M$ contains a closed essential surface of negative Euler characteristic or not depends on the difference of Seifert fibrations from the two sides of a torus system which splits $M$ into Seifert manifolds. However, it is not easy to characterize geometrically the class of irreducible graph manifolds which contain such surfaces. This article studies this problem in the case of graph link exteriors. Keywords:Graph link, Graph manifold, Seifert manifold, Essential surfaceCategory:57M25

32. CMB 2008 (vol 51 pp. 508)

Cavicchioli, Alberto; Spaggiari, Fulvia
 A Result in Surgery Theory We study the topological $4$-dimensional surgery problem for a closed connected orientable topological $4$-manifold $X$ with vanishing second homotopy and $\pi_1(X)\cong A * F(r)$, where $A$ has one end and $F(r)$ is the free group of rank $r\ge 1$. Our result is related to a theorem of Krushkal and Lee, and depends on the validity of the Novikov conjecture for such fundamental groups. Keywords:four-manifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly mapCategories:57N65, 57R67, 57Q10

33. CMB 2008 (vol 51 pp. 535)

Csorba, Péter
 On the Simple $\Z_2$-homotopy Types of Graph Complexes and Their Simple $\Z_2$-universality We prove that the neighborhood complex $\N(G)$, the box complex $\B(G)$, the homomorphism complex $\Hom(K_2,G)$and the Lov\'{a}sz complex $\L(G)$ have the same simple $\Z_2$-homotopy type in the sense of Whitehead. We show that these graph complexes are simple $\Z_2$-universal. Keywords:graph complexes, simple $\Z_2$-homotopy, universalityCategories:57Q10, 05C10, 55P10

34. CMB 2007 (vol 50 pp. 481)

Blanlœil, Vincent; Saeki, Osamu
 Concordance des nÅuds de dimension $4$ We prove that for a simply connected closed $4$-dimensional manifold, its embeddings into the sphere of dimension $6$ are all concordant to each other. Keywords:concordance, cobordisme, n{\oe}ud de dimension $4$, chirurgie plongÃ©eCategories:57Q45, 57Q60, 57R40, 57R65, 57N13

35. CMB 2007 (vol 50 pp. 390)

Hebda, James J.; Hsieh, Chun-Chung; Tsau, Chichen M.
 Linking Number of Singular Links and the Seifert Matrix We extend the notion of linking number of an ordinary link of two components to that of a singular link with transverse intersections in which case the linking number is a half-integer. We then apply it to simplify the construction of the Seifert matrix, and therefore the Alexander polynomial, in a natural way. Category:57M25

36. CMB 2007 (vol 50 pp. 365)

Godinho, Leonor
 Equivariant Cohomology of $S^{1}$-Actions on $4$-Manifolds Let $M$ be a symplectic $4$-dimensional manifold equipped with a Hamiltonian circle action with isolated fixed points. We describe a method for computing its integral equivariant cohomology in terms of fixed point data. We give some examples of these computations. Categories:53D20, 55N91, 57S15

37. CMB 2007 (vol 50 pp. 206)

Golasiński, Marek; Gonçalves, Daciberg Lima
 Spherical Space Forms: Homotopy Types and Self-Equivalences for the Group $({\mathbb Z}/a\rtimes{\mathbb Z}/b) \times SL_2\,(\mathbb{F}_p)$ Let $G=({\mathbb Z}/a\rtimes{\mathbb Z}/b) \times \SL_2(\mathbb{F}_p)$, and let $X(n)$ be an $n$-dimensional $CW$-complex of the homotopy type of an $n$-sphere. We study the automorphism group $\Aut (G)$ in order to compute the number of distinct homotopy types of spherical space forms with respect to free and cellular $G$-actions on all $CW$-complexes $X(2dn-1)$, where $2d$ is the period of $G$. The groups ${\mathcal E}(X(2dn-1)/\mu)$ of self homotopy equivalences of space forms $X(2dn-1)/\mu$ associated with free and cellular $G$-actions $\mu$ on $X(2dn-1)$ are determined as well. Keywords:automorphism group, $CW$-complex, free and cellular $G$-action, group of self homotopy equivalences, Lyndon--Hochschild--Serre spectral sequence, special (linear) group, spherical space formCategories:55M35, 55P15, 20E22, 20F28, 57S17

38. CMB 2006 (vol 49 pp. 624)

Teragaito, Masakazu
 On Non-Integral Dehn Surgeries Creating Non-Orientable Surfaces For a non-trivial knot in the $3$-sphere, only integral Dehn surgery can create a closed $3$-manifold containing a projective plane. If we restrict ourselves to hyperbolic knots, the corresponding claim for a Klein bottle is still true. In contrast to these, we show that non-integral surgery on a hyperbolic knot can create a closed non-orientable surface of any genus greater than two. Keywords:knot, Dehn surgery, non-orientable surfaceCategory:57M25

39. CMB 2006 (vol 49 pp. 337)

Berlanga, R.
 Homotopy Equivalence and Groups of Measure-Preserving Homeomorphisms It is shown that the group of compactly supported, measure-preserving homeomorphisms of a connected, second countable manifold is locally contractible in the direct limit topology. Furthermore, this group is weakly homotopically equivalent to the more general group of compactly supported homeomorphisms. Categories:57S05, 58F11

40. CMB 2006 (vol 49 pp. 55)

Dubois, Jérôme
 Non Abelian Twisted Reidemeister Torsion for Fibered Knots In this article, we give an explicit formula to compute the non abelian twisted sign-deter\-mined Reidemeister torsion of the exterior of a fibered knot in terms of its monodromy. As an application, we give explicit formulae for the non abelian Reidemeister torsion of torus knots and of the figure eight knot. Keywords:Reidemeister torsion, Fibered knots, Knot groups, Representation space, $\SU$, $\SL$, Adjoint representation, MonodromyCategories:57Q10, 57M27, 57M25

41. CMB 2006 (vol 49 pp. 36)

Daskalopoulos, Georgios D.; Wentworth, Richard A.
 Holomorphic Frames for Weakly Converging Holomorphic Vector Bundles Using a modification of Webster's proof of the Newlander--Nirenberg theorem, it is shown that, for a weakly convergent sequence of integrable unitary connections on a complex vector bundle over a complex manifold, there is a subsequence of local holomorphic frames that converges strongly in an appropriate Holder class. Categories:57M50, 58E20, 53C24

42. CMB 2005 (vol 48 pp. 547)

Fehér, L. M.; Némethi, A.; Rimányi, R.
 Degeneracy of 2-Forms and 3-Forms We study some global aspects of differential complex 2-forms and 3-forms on complex manifolds. We compute the cohomology classes represented by the sets of points on a manifold where such a form degenerates in various senses, together with other similar cohomological obstructions. Based on these results and a formula for projective representations, we calculate the degree of the projectivization of certain orbits of the representation $\Lambda^k\C^n$. Keywords:Classes of degeneracy loci, 2-forms, 3-forms, Thom polynomials, global singularity theoryCategories:14N10, 57R45

43. CMB 2005 (vol 48 pp. 32)

Dąbkowski, Mieczysław K.; Przytycki, Józef H.; Togha, Amir A.
 Non-Left-Orderable 3-Manifold Groups We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched coverings of $S^3$ branched along links. The figure eight knot provides simple nontrivial examples. The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold branched covers of $S^3$ branched along various hyperbolic 2-bridge knots. %with various hyperbolic 2-bridge knots as branched sets. The manifold obtained in such a way from the $5_2$ knot is of special interest as it is conjectured to be the hyperbolic 3-manifold with the smallest volume. Categories:57M25, 57M12, 20F60

44. CMB 2004 (vol 47 pp. 332)

Charette, Virginie; Goldman, William M.; Jones, Catherine A.
 Recurrent Geodesics in Flat Lorentz $3$-Manifolds Let $M$ be a complete flat Lorentz $3$-manifold $M$ with purely hyperbolic holonomy $\Gamma$. Recurrent geodesic rays are completely classified when $\Gamma$ is cyclic. This implies that for any pair of periodic geodesics $\gamma_1$, $\gamma_2$, a unique geodesic forward spirals towards $\gamma_1$ and backward spirals towards $\gamma_2$. Keywords:geometric structures on low-dimensional manifolds, notions of recurrenceCategories:57M50, 37B20

45. CMB 2004 (vol 47 pp. 439)

Parker, John R.
 On the Stable Basin Theorem The stable basin theorem was introduced by Basmajian and Miner as a key step in their necessary condition for the discreteness of a non-elementary group of complex hyperbolic isometries. In this paper we improve several of Basmajian and Miner's key estimates and so give a substantial improvement on the main inequality in the stable basin theorem. Categories:22E40, 20H10, 57S30

46. CMB 2004 (vol 47 pp. 60)

Little, Robert D.
 Rational Integer Invariants of Regular Cyclic Actions Let $g\colon M^{2n}\rightarrow M^{2n}$ be a smooth map of period $m>2$ which preserves orientation. Suppose that the cyclic action defined by $g$ is regular and that the normal bundle of the fixed point set $F$ has a $g$-equivariant complex structure. Let $F\pitchfork F$ be the transverse self-intersection of $F$ with itself. If the $g$-signature $\Sign (g,M)$ is a rational integer and $n<\phi (m)$, then there exists a choice of orientations such that $\Sign(g,M)= \Sign F=\Sign(F\pitchfork F)$. Category:57S17

47. CMB 2003 (vol 46 pp. 617)

Pak, Hong Kyung
 On Harmonic Theory in Flows Recently [8], a harmonic theory was developed for a compact contact manifold from the viewpoint of the transversal geometry of contact flow. A contact flow is a typical example of geodesible flow. As a natural generalization of the contact flow, the present paper develops a harmonic theory for various flows on compact manifolds. We introduce the notions of $H$-harmonic and $H^*$-harmonic spaces associated to a H\"ormander flow. We also introduce the notions of basic harmonic spaces associated to a weak basic flow. One of our main results is to show that in the special case of isometric flow these harmonic spaces are isomorphic to the cohomology spaces of certain complexes. Moreover, we find an obstruction for a geodesible flow to be isometric. Keywords:contact structure, geodesible flow, isometric flow, basic cohomologyCategories:53C20, 57R30

48. CMB 2003 (vol 46 pp. 356)

Ishiwata, Makiko; Przytycki, Józef H.; Yasuhara, Akira
 Branched Covers of Tangles in Three-balls We give an algorithm for a surgery description of a $p$-fold cyclic branched cover of $B^3$ branched along a tangle. We generalize constructions of Montesinos and Akbulut-Kirby. Keywords:tangle, branched cover, surgery, Heegaard decompositionCategories:57M25, 57M12

49. CMB 2003 (vol 46 pp. 310)

Wang, Xiaofeng
 Second Order Dehn Functions of Asynchronously Automatic Groups Upper bounds of second order Dehn functions of asynchronously automatic groups are obtained. Keywords:second order Dehn function, combing, asynchronously automatic groupCategories:20E06, 20F05, 57M05

50. CMB 2003 (vol 46 pp. 265)

Oh, Seungsang
 Reducing Spheres and Klein Bottles after Dehn Fillings Let $M$ be a compact, connected, orientable, irreducible 3-manifold with a torus boundary. It is known that if two Dehn fillings on $M$ along the boundary produce a reducible manifold and a manifold containing a Klein bottle, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result. Keywords:Dehn filling, reducible, Klein bottleCategory:57M50
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