- the connected sum of three real projective planes (thus of a Klein bottle and a projective plane) is topologically equivalent to the sum of a torus and a real projective plane: ; we get Dyck's surface.The classification theorem of compact surfaces without boundaries states that such a surf...
Let Sigma(g,n) be an orientable surface with genus g >= 2 bordered by n >= 1 curves homeomorphic to circle. As is well known that one-holed torus Sigma(1,1) is the building block of such surfaces. By using the notion of symplectic chain complex, homological algebra techniques and ...
The sphere and the torus have Euler characteristics 2 and 0, respectively, and in general the Euler characteristic of the connected sum of g tori is 2 − 2g. La sfero kaj la toro havas eŭlerajn karakterizojn 2 kaj 0 respektive, kaj tiel plu eŭlera karakterizo de la koneksa ...
Heegaard Splittings of Twisted Torus Knots Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard spli... Y Moriah,E Sedgwick - 《Topology & Its Applications》 被引量: 18发表: 2009年 CLOSED ESSENTIAL ...
- 《Journal of Knot Theory & Its Ramifications》 被引量: 8发表: 2009年 The SU(3) Casson invariant for 3-manifolds split along a 2-sphere or a 2-torus The first is a connected sum formula for the SU(3) Casson invariant [J. Differential Geom. 53 (1999) 443–465]. The second ...
In previous work, we dealt only with disjoint unions, and ignored the relationship between the stably complex structure and the action of the torus. In passing, we introduce a notion of connected sum # for simple n-dimensional polytopes; when Pn is a product of simplices, we describe Pn #...
Does Borsuk Ulam Theorem hold for torus? Suppose A and B are both connected subsets of the same metric space, and A intersection B not equal to theta. (a) Prove that A union B is connected . (b) Is A intersection B necessarily connected? (Hi ...
f. Then the mapping torus T(α) is in a natural way a finite CW-complex. Choose any homotopy equivalence Φ: T(α) → X× S1 and let Ψ be a homotopy inverse of Φ. Define the involution λ:X×S1→X×S1,λ(x,z)=(x,z¯), and put...
The aim of this thesis is to introduce mathematical structures that can be e... P Raumonen 被引量: 17发表: 2009年 An Orlik-Raymond type classification of simply connected six-dimensional torus manifolds with vanishing odd degree cohomology The aim of this paper is to classify simply connected...
We consider the moduli space of flat G-bundles over the twodimensional torus, where G is a real, compact, simple Lie group which is not simply connected. We show that the connected components that describe topologically non-trivial bundles are isomorphic as symplectic spaces to moduli spaces of...