Extends G-signature theorem to Witt G-pseudomanifolds.
problem Computing G-signature for Witt G-pseudomanifolds.
method Intersection cohomology and fixed point set analysis.
result Formula for G-signature at fixed points of Witt G-pseudomanifolds.
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12 results for “G-signature”
Defines knot signature invariant using G-signature theorem.
problem No specific problem stated; focuses on knot theory.
method Uses G-signature theorem to define knot invariant.
result Defines an invariant for strongly invertible knots.
Let G be a finite group. To every smooth G-action on a compact, connected and oriented surface we can associate its data of singular orbits. The set of such data becomes an Abelian group B_G under the G-equivariant connected sum. We will show that the map which sends G to B_G is functorial and carries many features of …
New findings on knot genera using advanced techniques.
problem Understanding the 4-genus of knots, especially strongly invertible and periodic ones.
method Innovative concordance group invariants, Donaldson's theorem, and g-signature.
result Many new examples showing the equivariant 4-genus is larger than the 4-genus.
In a strengthening of the G-Signature Theorem of Atiyah and Singer, we compute, at least in principle (modulo certain torsion of exponent dividing a power of the order of G), the class in equivariant K-homology of the signature operator on a G-manifold, localized at a prime idea of R(G), in terms of the classes in non-…
Proves uniqueness of certain -symmetric gravitational instantons.
problem Proving uniqueness of -symmetric gravitational instantons.
method Using a divergence identity and results from the -signature theorem.
result Proof of the -symmetric Euclidean Black Hole Uniqueness conjecture.
We prove a Hitchin-Thorpe inequality for noncompact 4-manifolds with foliated geometry at infinity by extending on previous work by Dai and Wei. After introducing the objects at hand, we recall some preliminary results regarding the -signature formula and the rho invariant, which are used to obtain expressions for t…
Kawakubo and Uchida showed that, if a closed oriented -dimensional manifold admits a semi-free circle action such that the dimension of the fixed point set is less than , then the signature of vanishes. In this note, by using -signature theorem and the rigidity of the signature operator, we generaliz…
This paper describes a topological method to compute the spectral flow of a family of twisted Dirac operators, it includes two detailed examples. Briefly, a formula of Atiyah, Patodi and Singer expresses the spectral flow in terms of Chern-Simons invariants and rho invariants. The first step is to construct a flat cobo…
We develop obstructions to a knot K in the 3-sphere bounding a smooth punctured Klein bottle in the 4-ball. The simplest of these is based on the linking form of the 2-fold branched cover of the 3-sphere branched over K. Stronger obstructions are based on the Ozsvath-Szabo correction term in Heegaard-Floer homology, al…
In this paper, we use `generalized Seifert surfaces' to extend the Levine-Tristram signature to colored links in S^3. This yields an integral valued function on the m-dimensional torus, where m is the number of colors of the link. The case m=1 corresponds to the Levine-Tristram signature. We show that many remarkable p…
Study on constraints for topological and smooth realizations of line arrangements and configurations.
problem Investigating constraints on topological and smooth realizations of combinatorial line arrangements and -configurations.
method Exploring constraints via locally-flatly or smoothly embedded 2-spheres, using Furuta's 10/8-Theorem, and G-signature theorem.
result Established a new lower bound for -configurations, showing for topological realizations.