scholarly journals The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifold

2008 ◽  
pp. 1-20
Author(s):  
Andrew Haas
Keyword(s):  
Cone Singularity

The Icecream‐Cone Singularity in S‐Matrix Theory

1966 ◽  
Vol 7 (9) ◽  
pp. 1600-1606 ◽  
Author(s):  
P. V. Landshoff ◽  
D. I. Olive ◽  
J. C. Polkinghorne
Keyword(s):  
Matrix Theory ◽  
S Matrix ◽  
Cone Singularity

scholarly journals Curvature, cones and characteristic numbers

2013 ◽  
Vol 155 (1) ◽  
pp. 13-37 ◽  
Author(s):  
MICHAEL ATIYAH ◽  
CLAUDE LEBRUN
Keyword(s):  
Einstein Metrics ◽  
Cone Angle ◽  
Gravitational Instantons ◽  
Characteristic Numbers ◽  
Cone Singularity ◽  
Integral Formulae ◽  
Do So

AbstractWe study Einstein metrics on smooth compact 4-manifolds with an edge-cone singularity of specified cone angle along an embedded 2-manifold. To do so, we first derive modified versions of the Gauss–Bonnet and signature theorems for arbitrary Riemannian 4-manifolds with edge-cone singularities, and then show that these yield non-trivial obstructions in the Einstein case. We then use these integral formulæ to obtain interesting information regarding gravitational instantons which arise as limits of such edge-cone manifolds.

scholarly journals Signatures of Topological Branched Covers

2020 ◽  
Author(s):  
Christian Geske ◽  
Alexandra Kjuchukova ◽  
Julius L Shaneson
Keyword(s):  
Smooth Point ◽  
New Technique ◽  
Intersection Homology ◽  
Smooth Manifolds ◽  
Branched Covers ◽  
Branched Cover ◽  
Stratified Pseudomanifold ◽  
A New Technique ◽  
Cone Singularity

Abstract Let $X^4$ and $Y^4$ be smooth manifolds and $f: X\to Y$ a branched cover with branching set $B$. Classically, if $B$ is smoothly embedded in $Y$, the signature $\sigma (X)$ can be computed from data about $Y$, $B$ and the local degrees of $f$. When $f$ is an irregular dihedral cover and $B\subset Y$ smoothly embedded away from a cone singularity whose link is $K$, the second author gave a formula for the contribution $\Xi (K)$ to $\sigma (X)$ resulting from the non-smooth point. We extend the above results to the case where $Y$ is a topological four-manifold and $B$ is locally flat, away from the possible singularity. Owing to the presence of points on $B$ which are not locally flat, $X$ in this setting is a stratified pseudomanifold, and we use the intersection homology signature of $X$, $\sigma _{IH}(X)$. For any knot $K$ whose determinant is not $\pm 1$, a homotopy ribbon obstruction is derived from $\Xi (K)$, providing a new technique to potentially detect slice knots that are not ribbon.

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