location:  Publications → journals
Search results

Search: MSC category 57 ( Manifolds and cell complexes )

 Expand all        Collapse all Results 26 - 41 of 41

26. CJM 2003 (vol 55 pp. 1080)

Kellerhals, Ruth
 Quaternions and Some Global Properties of Hyperbolic $5$-Manifolds We provide an explicit thick and thin decomposition for oriented hyperbolic manifolds $M$ of dimension $5$. The result implies improved universal lower bounds for the volume $\rmvol_5(M)$ and, for $M$ compact, new estimates relating the injectivity radius and the diameter of $M$ with $\rmvol_5(M)$. The quantification of the thin part is based upon the identification of the isometry group of the universal space by the matrix group $\PS_\Delta {\rm L} (2,\mathbb{H})$ of quaternionic $2\times 2$-matrices with Dieudonn\'e determinant $\Delta$ equal to $1$ and isolation properties of $\PS_\Delta {\rm L} (2,\mathbb{H})$. Categories:53C22, 53C25, 57N16, 57S30, 51N30, 20G20, 22E40

27. CJM 2003 (vol 55 pp. 766)

Kerler, Thomas
 Homology TQFT's and the Alexander--Reidemeister Invariant of 3-Manifolds via Hopf Algebras and Skein Theory We develop an explicit skein-theoretical algorithm to compute the Alexander polynomial of a 3-manifold from a surgery presentation employing the methods used in the construction of quantum invariants of 3-manifolds. As a prerequisite we establish and prove a rather unexpected equivalence between the topological quantum field theory constructed by Frohman and Nicas using the homology of $U(1)$-representation varieties on the one side and the combinatorially constructed Hennings TQFT based on the quasitriangular Hopf algebra $\mathcal{N} = \mathbb{Z}/2 \ltimes \bigwedge^* \mathbb{R}^2$ on the other side. We find that both TQFT's are $\SL (2,\mathbb{R})$-equivariant functors and, as such, are isomorphic. The $\SL (2,\mathbb{R})$-action in the Hennings construction comes from the natural action on $\mathcal{N}$ and in the case of the Frohman--Nicas theory from the Hard--Lefschetz decomposition of the $U(1)$-moduli spaces given that they are naturally K\"ahler. The irreducible components of this TQFT, corresponding to simple representations of $\SL(2,\mathbb{Z})$ and $\Sp(2g,\mathbb{Z})$, thus yield a large family of homological TQFT's by taking sums and products. We give several examples of TQFT's and invariants that appear to fit into this family, such as Milnor and Reidemeister Torsion, Seiberg--Witten theories, Casson type theories for homology circles {\it \a la} Donaldson, higher rank gauge theories following Frohman and Nicas, and the $\mathbb{Z}/p\mathbb{Z}$ reductions of Reshetikhin--Turaev theories over the cyclotomic integers $\mathbb{Z} [\zeta_p]$. We also conjecture that the Hennings TQFT for quantum-$\mathfrak{sl}_2$ is the product of the Reshetikhin--Turaev TQFT and such a homological TQFT. Categories:57R56, 14D20, 16W30, 17B37, 18D35, 57M27

28. CJM 2003 (vol 55 pp. 636)

Schwartzman, Sol
 Higher Dimensional Asymptotic Cycles Given a $p$-dimensional oriented foliation of an $n$-dimensional compact manifold $M^n$ and a transversal invariant measure $\tau$, Sullivan has defined an element of $H_p (M^n,R)$. This generalized the notion of a $\mu$-asymptotic cycle, which was originally defined for actions of the real line on compact spaces preserving an invariant measure $\mu$. In this one-dimensional case there was a natural 1--1 correspondence between transversal invariant measures $\tau$ and invariant measures $\mu$ when one had a smooth flow without stationary points. For what we call an oriented action of a connected Lie group on a compact manifold we again get in this paper such a correspondence, provided we have what we call a positive quantifier. (In the one-dimensional case such a quantifier is provided by the vector field defining the flow.) Sufficient conditions for the existence of such a quantifier are given, together with some applications. Categories:57R30, 57S20

29. CJM 2002 (vol 54 pp. 396)

Lebel, André
 Framed Stratified Sets in Morse Theory In this paper, we present a smooth framework for some aspects of the geometry of CW complexes'', in the sense of Buoncristiano, Rourke and Sanderson \cite{[BRS]}. We then apply these ideas to Morse theory, in order to generalize results of Franks \cite{[F]} and Iriye-Kono \cite{[IK]}. More precisely, consider a Morse function $f$ on a closed manifold $M$. We investigate the relations between the attaching maps in a CW complex determined by $f$, and the moduli spaces of gradient flow lines of $f$, with respect to some Riemannian metric on~$M$. Categories:57R70, 57N80, 55N45

30. CJM 2001 (vol 53 pp. 1309)

Steer, Brian; Wren, Andrew
 The Donaldson-Hitchin-Kobayashi Correspondence for Parabolic Bundles over Orbifold Surfaces A theorem of Donaldson on the existence of Hermitian-Einstein metrics on stable holomorphic bundles over a compact K\"ahler surface is extended to bundles which are parabolic along an effective divisor with normal crossings. Orbifold methods, together with a suitable approximation theorem, are used following an approach successful for the case of Riemann surfaces. Categories:14J17, 57R57

31. CJM 2001 (vol 53 pp. 780)

Nicolaescu, Liviu I.
 Seiberg-Witten Invariants of Lens Spaces We show that the Seiberg-Witten invariants of a lens space determine and are determined by its Casson-Walker invariant and its Reidemeister-Turaev torsion. Keywords:lens spaces, Seifert manifolds, Seiberg-Witten invariants, Casson-Walker invariant, Reidemeister torsion, eta invariants, Dedekind-Rademacher sumsCategories:58D27, 57Q10, 57R15, 57R19, 53C20, 53C25

32. CJM 2001 (vol 53 pp. 212)

Puppe, V.
 Group Actions and Codes A $\mathbb{Z}_2$-action with maximal number of isolated fixed points'' ({\it i.e.}, with only isolated fixed points such that $\dim_k (\oplus_i H^i(M;k)) =|M^{\mathbb{Z}_2}|, k = \mathbb{F}_2)$ on a $3$-dimensional, closed manifold determines a binary self-dual code of length $=|M^{\mathbb{Z}_2}|$. In turn this code determines the cohomology algebra $H^*(M;k)$ and the equivariant cohomology $H^*_{\mathbb{Z}_2}(M;k)$. Hence, from results on binary self-dual codes one gets information about the cohomology type of $3$-manifolds which admit involutions with maximal number of isolated fixed points. In particular, most'' cohomology types of closed $3$-manifolds do not admit such involutions. Generalizations of the above result are possible in several directions, {\it e.g.}, one gets that most'' cohomology types (over $\mathbb{F}_2)$ of closed $3$-manifolds do not admit a non-trivial involution. Keywords:Involutions, $3$-manifolds, codesCategories:55M35, 57M60, 94B05, 05E20

33. CJM 2000 (vol 52 pp. 293)

Collin, Olivier
 Floer Homology for Knots and $\SU(2)$-Representations for Knot Complements and Cyclic Branched Covers In this article, using 3-orbifolds singular along a knot with underlying space a homology sphere $Y^3$, the question of existence of non-trivial and non-abelian $\SU(2)$-representations of the fundamental group of cyclic branched covers of $Y^3$ along a knot is studied. We first use Floer Homology for knots to derive an existence result of non-abelian $\SU(2)$-representations of the fundamental group of knot complements, for knots with a non-vanishing equivariant signature. This provides information on the existence of non-trivial and non-abelian $\SU(2)$-representations of the fundamental group of cyclic branched covers. We illustrate the method with some examples of knots in $S^3$. Categories:57R57, 57M12, 57M25, 57M05

34. CJM 1999 (vol 51 pp. 1035)

Litherland, R. A.
 The Homology of Abelian Covers of Knotted Graphs Let $\tilde M$ be a regular branched cover of a homology 3-sphere $M$ with deck group $G\cong \zt^d$ and branch set a trivalent graph $\Gamma$; such a cover is determined by a coloring of the edges of $\Gamma$ with elements of $G$. For each index-2 subgroup $H$ of $G$, $M_H = \tilde M/H$ is a double branched cover of $M$. Sakuma has proved that $H_1(\tilde M)$ is isomorphic, modulo 2-torsion, to $\bigoplus_H H_1(M_H)$, and has shown that $H_1(\tilde M)$ is determined up to isomorphism by $\bigoplus_H H_1(M_H)$ in certain cases; specifically, when $d=2$ and the coloring is such that the branch set of each cover $M_H\to M$ is connected, and when $d=3$ and $\Gamma$ is the complete graph $K_4$. We prove this for a larger class of coverings: when $d=2$, for any coloring of a connected graph; when $d=3$ or $4$, for an infinite class of colored graphs; and when $d=5$, for a single coloring of the Petersen graph. Categories:57M12, 57M25, 57M15

35. CJM 1999 (vol 51 pp. 585)

Mansfield, R.; Movahedi-Lankarani, H.; Wells, R.
 Smooth Finite Dimensional Embeddings We give necessary and sufficient conditions for a norm-compact subset of a Hilbert space to admit a $C^1$ embedding into a finite dimensional Euclidean space. Using quasibundles, we prove a structure theorem saying that the stratum of $n$-dimensional points is contained in an $n$-dimensional $C^1$ submanifold of the ambient Hilbert space. This work sharpens and extends earlier results of G.~Glaeser on paratingents. As byproducts we obtain smoothing theorems for compact subsets of Hilbert space and disjunction theorems for locally compact subsets of Euclidean space. Keywords:tangent space, diffeomorphism, manifold, spherically compact, paratingent, quasibundle, embeddingCategories:57R99, 58A20

36. CJM 1998 (vol 50 pp. 620)

Sjerve, Denis; Yang, Qing Jie
 The Eichler trace of $\bbd Z_p$ actions on Riemann surfaces We study $\hbox{\Bbbvii Z}_p$ actions on compact connected Riemann surfaces via their associated Eichler traces. We determine the set of possible Eichler traces and determine the relationship between 2 actions if they have the same trace. Categories:30F30, 57M60

37. CJM 1998 (vol 50 pp. 581)

Kamiyama, Yasuhiko
 The homology of singular polygon spaces Let $M_n$ be the variety of spatial polygons $P= (a_1, a_2, \dots, a_n)$ whose sides are vectors $a_i \in \text{\bf R}^3$ of length $\vert a_i \vert=1 \; (1 \leq i \leq n),$ up to motion in $\text{\bf R}^3.$ It is known that for odd $n$, $M_n$ is a smooth manifold, while for even $n$, $M_n$ has cone-like singular points. For odd $n$, the rational homology of $M_n$ was determined by Kirwan and Klyachko [6], [9]. The purpose of this paper is to determine the rational homology of $M_n$ for even $n$. For even $n$, let ${\tilde M}_n$ be the manifold obtained from $M_n$ by the resolution of the singularities. Then we also determine the integral homology of ${\tilde M}_n$. Keywords:singular polygon space, homologyCategories:14D20, 57N65

38. CJM 1997 (vol 49 pp. 1323)

Sankaran, Parameswaran; Zvengrowski, Peter
 Stable parallelizability of partially oriented flag manifolds II In the first paper with the same title the authors were able to determine all partially oriented flag manifolds that are stably parallelizable or parallelizable, apart from four infinite families that were undecided. Here, using more delicate techniques (mainly K-theory), we settle these previously undecided families and show that none of the manifolds in them is stably parallelizable, apart from one 30-dimensional manifold which still remains undecided. Categories:57R25, 55N15, 53C30

39. CJM 1997 (vol 49 pp. 883)

Okounkov, Andrei
 Proof of a conjecture of Goulden and Jackson We prove an integration formula involving Jack polynomials conjectured by I.~P.~Goulden and D.~M.~Jackson in connection with enumeration of maps in surfaces. Categories:05E05, 43A85, 57M15

40. CJM 1997 (vol 49 pp. 696)

Charitos, Charalambos; Tsapogas, Georgios
 Geodesic flow on ideal polyhedra In this work we study the geodesic flow on $n$-dimensional ideal polyhedra and establish classical (for manifolds of negative curvature) results concerning the distribution of closed orbits of the flow. Categories:57M20, 53C23

41. CJM 1997 (vol 49 pp. 193)

Casali, Maria Rita
 Classifying PL $5$-manifolds by regular genus: the boundary case In the present paper, we face the problem of classifying classes of orientable PL $5$-manifolds $M^5$ with $h \geq 1$ boundary components, by making use of a combinatorial invariant called {\it regular genus} ${\cal G}(M^5)$. In particular, a complete classification up to regular genus five is obtained: $${\cal G}(M^5) = \gG \leq 5 \Longrightarrow M^5 \cong \#_{\varrho - \gbG}(\bdo) \# \smo_{\gbG},$$ where $\gbG = {\cal G}(\partial M^5)$ denotes the regular genus of the boundary $\partial M^5$ and $\smo_{\gbG}$ denotes the connected sum of $h\geq 1$ orientable $5$-dimensional handlebodies $\cmo_{\alpha_i}$ of genus $\alpha_i\geq 0$ ($i=1,\ldots, h$), so that $\sum_{i=1}^h \alpha_i = \gbG.$ \par Moreover, we give the following characterizations of orientable PL $5$-manifolds $M^5$ with boundary satisfying particular conditions related to the `gap'' between ${\cal G}(M^5)$ and either ${\cal G}(\partial M^5)$ or the rank of their fundamental group $\rk\bigl(\pi_1(M^5)\bigr)$: $$\displaylines{{\cal G}(\partial M^5)= {\cal G}(M^5) = \varrho \Longleftrightarrow M^5 \cong \smo_{\gG}\cr {\cal G}(\partial M^5)= \gbG = {\cal G}(M^5)-1 \Longleftrightarrow M^5 \cong (\bdo) \# \smo_{\gbG}\cr {\cal G}(\partial M^5)= \gbG = {\cal G}(M^5)-2 \Longleftrightarrow M^5 \cong \#_2 (\bdo) \# \smo_{\gbG}\cr {\cal G}(M^5) = \rk\bigl(\pi_1(M^5)\bigr)= \varrho \Longleftrightarrow M^5 \cong \#_{\gG - \gbG}(\bdo) \# \smo_{\gbG}.\cr}$$ \par Further, the paper explains how the above results (together with other known properties of regular genus of PL manifolds) may lead to a combinatorial approach to $3$-dimensional Poincar\'e Conjecture. Categories:57N15, 57Q15, 05C10
 Page Previous 1 2
 top of page | contact us | privacy | site map |