Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 16 of 16 for “"Equivariant Cohomology"”.
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Gauge-fixing and equivariant cohomology
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.
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Equivariant cohomology, homogeneous spaces and graphs
… We investigate the relationship between the equivariant cohomology of the manifold M and the fixed point data of the torus action. We are interested in understanding the topology of the space of T-orbits in M. In particular, we explore aspects of this topology which are determined by data …
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Equivariant cohomology and smooth p-toral actions
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1980
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On the Quantum Cohomology of Fano Toric Manifolds and the Intersection Cohomology of Singular Symplectic Quotients
The second result computes the intersection cohomology of the singular symplectic reduced spaces. Let M be a closed symplectic manifold with a Hamiltonian S1-action defined on it and mu is the moment map. If 0 is a singular value of mu, the reduced space mu-1(0)/S1 is, in general, no longer an …
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Some results related to the quantum geometric Langlands program
… spherical perverse sheaves sits naturally in an equivariant derived category, and this larger category was described in terms of the dual group by Bezrukavnikov-Finkelberg. Recently, Finkelberg-Lysenko proved a "twisted" version of the geometric Satake equivalence, which involves perverse sheaves …
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Semi-Free Hamiltonian Circle Actions on Six-Dimensional Symplectic Manifolds
… list of the possible manifolds, determine their equivariant cohomology ring and equivariant Chern classes. We classify some of these manifolds up to diffeomorphism. We also show the existence of most of these manifolds.
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The topology of GKM spaces and GKM fibrations
… can be used to simplify the computation of the equivariant cohomology of a GKM space. In particular we investigate the role that equivariant maps play in the computation of these cohomology rings. In the first part of the thesis, we describe some implications of the existence of an equivariant …
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Cotangent Schubert Calculus in Grassmannians
… Segre-MacPherson classes of Schubert cells in T-equivariant cohomology and the motivic Segre classes of Schubert cells in T-equivariant K-theory. In doing so we look at the pushforward of the projection map from the Bott-Samelson (Kempf-Laksov) desingularization to the Grassmannian. We find that …
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Quasi-elliptic cohomology
We introduce and study quasi-elliptic cohomology, a theory related to Tate K-theory but built over the ring $\mathbb{Z}[q^{\pm}]$. In Chapter 2 we build an orbifold version of the theory, inspired by Devoto's equivariant Tate K-theory. In Chapter 3 we construct power operation in the orbifold …
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Matrix Schubert varieties for the affine Grassmannian
… the multiplication of Schubert classes in the cohomology of flag varieties, and is typically conducted using algebraic combinatorics by way of a polynomial ring presentation of the cohomology ring. The polynomials that represent the Schubert classes are called Schubert polynomials. An ongoing …
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Categorification of the Kirwan map
… it follows that we have a map from the equivariant cohomology of the scheme to the cohomology of the quotient. It is natural to ask if this map is surjective. This question is known as Kirwan surjectivity. There is much literature surrounding this question but the exact boundary of when …
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GKM manifolds with low Betti numbers
… information of the manifold, in particular the equivariant cohomology and Chern classes. We are interested in the case where the torus action is Hamiltonian. In this thesis we will consider the case where the GKM graphs are complete. When the dimension of the torus action is sufficiently large, …
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Two-dimensional twisted sigma models and chiral differential operators
… at a purely physical interpretation of the equivariant cohomology of the CDR, recently defined by mathematicians, called the a??chiral equivariant cohomologya??.Via the math-physics connection unveiled, we find that various physical features of the above sigma models can be described in …
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Equivariant Schubert calculus and applications
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms
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Towards studying of the higher rank theory of stable pairs
This thesis is composed of two parts. In the first part we introduce a higher rank analog of the Pandharipande-Thomas theory of stable pairs on a Calabi-Yau threefold $X$. More precisely, we develop a moduli theory for frozen triples given by the data $\mathcal{O}_X^{\oplus r}(-n)\xrightarrow{\phi} …
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Splines on polytopal complexes
… theory and computer-aided geometric design to equivariant cohomology and GKM theory. A primary goal in approximation theory is to construct bases of the vector space $C^r_d(\PC)$ of splines of degree at most $d$ on $\PC$, although even computing the dimension of this space proves to be …