1,720,994 research outputs found
Some open problems in geometric topology of low dimensions
No full textWe study some open problems in geometric topolofy of low dimensions: the 2-sphere approximation conjecture, controlled isotopy, equivalent spines, cell-like resolutions, geometric presentations of manifold fundamental groups, classification of triangulated manifolds according to genus
PALINDROME PRESENTATIONS OF RATIONAL KNOTS
No full textWe give explicit palindrome presentations of the groups of rational knots, that is, presentations with relators which read the same forwards and backwards. This answers a question posed by Hilden, Tejada and Toro in 2002. Using such presentations we obtain simple alternative proofs of some classical results concerning the Alexander polynomial of all rational knots and the character variety of certain rational knots. Finally, we derive a new recursive description of the SL(2,C) character variety of twist knots
On a certain surgery spectral sequence
No full textGiven a morphism between twisted quadratic extensions of antistructures, we construct a spectral sequence which generalizes, in a natural way, the surgery spectral sequence introduced by Hambleton and Kharshiladze in Mat. sbornik 183 (1992). Our spectral sequence allows us to obtain some additional information about the Browder-Livesay invariants. Then we study the relations between the above-mentioned spectral sequences, and discuss some examples and applications
On 4-manifolds fibering over surfaces
No full textWe study closed connected topological or smooth 4-manifolds fibering over a surface in terms of classifying spaces, characteristic classes, and intersection forms
Applications of controlled surgery in dimension 4 : examples
Full text linkThe validity of Freedmans disc theorem is known to depend only on the fundamental group.It was conjectured that it fails for non abelian free fundamental groups.If this were true then surgery would work in dimension four.Recently,Krushkal and Lee proved a surprising result that surgery works for a large class of 4-manifolds with free nonabelian fundamental groups.The goal of this paper is to show that this is best understood using controlled surgery theor
On the stable classification of certain 4-manifolds
No full textWe study the s-cobordism type of closed orientable (smooth or PL) 4-manifolds with free or surface fundamental groups. We prove stable classification theorems for these classes of manifolds by using surgery theory
Special classes of closed four-manifolds
Full text linkWe present several results and state some open problems on the classification of topological and geometric structures of closed connected oriented (smooth) four-manifolds. In particular, we discuss many interesting classes of closed four-manifolds satisfying additional properties, that is, spin manifolds, manifolds with special homology (resp. homotopy), exact manifolds, geometric manifolds, and smooth manifolds. The results are obtained by using methods and techniques from algebraic and differential topology, and homological algebra
Four-manifolds with surface fundamental groups
No full textWe study the homotopy type of closed connected topological 4-manifolds whose fundamental group is that of an aspherical surface F. Then we use surgery theory to show that these manifolds are s-cobordant to connected sums of simply-connected manifolds with an S^2-bundle over F
On the construction of 4k-dimensional generalized manifolds
No full textWe construct 4k-dimensional generalized manifolds, for k greater than 1, which have no resolutions. The construction proceeds as in a paper of Bryant, Ferry, Mio and Weinberger, Ann. of Math. 143 (1996), but does not use their controlled (\epsilon, \delta)-surgery sequence
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