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Geometry and Topology, ISSN 1465-3060, 06/2018, Volume 22, Issue 5, pp. 2865 - 2942
Journal Article
02/2017
Geom. Topol. 22 (2018) 2865-2942 We study the Seiberg-Witten invariant $\lambda_{\rm{SW}} (X)$ of smooth spin $4$-manifolds $X$ with integral homology of... 
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 08/2017, Volume 58, Issue 8, p. 82301
We work on a parallelizable time-orientable Lorentzian 4-manifold and prove that in this case, the notion of spin structure can be equivalently defined in a... 
PHYSICS, MATHEMATICAL | SPECTRAL THEORETIC CHARACTERIZATION | Mathematical analysis | Spin structure | Differential equations
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 08/2017, Volume 58, Issue 8, p. 1
We work on a parallelizable time-orientable Lorentzian 4-manifold and prove that in this case, the notion of spin structure can be equivalently defined in a... 
Geometry | Topological manifolds | Mathematical analysis | Differential equations | Spin structure
Journal Article
Compositio Mathematica, ISSN 0010-437X, 02/2016, Volume 152, Issue 2, pp. 399 - 444
We extend the Atiyah, Patodi, and Singer index theorem for first-order differential operators from the context of manifolds with cylindrical ends to manifolds... 
positive scalar curvature | Fredholm operator | periodic end | Index theorem | index theorem | ETA-INVARIANTS | METRICS | DIRAC OPERATORS | MODULI SPACES | MATHEMATICS | OPEN MANIFOLDS | SPECTRAL ASYMMETRY | HEAT KERNEL | 4-MANIFOLDS | RIEMANNIAN GEOMETRY | Theorems | Algebra | Manifolds | Operators | Mathematical analysis | Scalars | Complement | Curvature
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 10/2011, Volume 154, Issue 1, pp. 93 - 101
We derive a formula for the $${\bar\mu}$$ -invariant of a Seifert fibered homology sphere in terms of the η-invariant of its Dirac operator. As a consequence,... 
Geometry | η -invariant | 57M27 | Seiberg–Witten equations | 57R57 | Mathematics | Dirac operator | Seifert fibered homology sphere | {\bar\mu}$$ -invariant | 11F20
Journal Article
Topology and its Applications, ISSN 0166-8641, 08/2016, Volume 209, pp. 134 - 152
The configuration space of ordered pairs of distinct points in a manifold , also known as the deleted square of , is not a homotopy invariant of : Longoni and... 
Lens space | Chern–Simons invariant | Configuration space | Cheeger–Simons character | Chern-Simons invariant | Cheeger-Simons character | MATHEMATICS | MATHEMATICS, APPLIED | CHERN-SIMONS INVARIANTS
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 09/2017, Volume 17, Issue 5, pp. 2635 - 2685
Singular instanton Floer homology was defined by Kronheimer and Mrowka in connection with their proof that Khovanov homology is an unknot detector. We study... 
FLOER HOMOLOGY | SURGERY | MATHEMATICS | INSTANTON HOMOLOGY | KNOT-GROUPS | INVARIANTS | SPHERES | BRANCHED COVERS | SPECTRAL ASYMMETRY | RIEMANNIAN GEOMETRY | REPRESENTATION SPACES | Mathematics - Geometric Topology
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2017, Volume 10388, pp. 336 - 348
Conference Proceeding
Journal of Differential Geometry, ISSN 0022-040X, 2011, Volume 88, Issue 2, pp. 333 - 377
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 04/2012, Volume 21, Issue 5, pp. 1250054 - 1250058
For any oriented link of two components in an integral homology 3-sphere, we define an instanton Floer homology whose Euler characteristic is twice the linking... 
link | Knot | linking number | Floer homology | instanton | MATHEMATICS | INVARIANT | EXTERIORS | Integrals | Links | Homology | Joining | Knot theory | Linking | Instantons
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 01/2015, Volume 14, Issue 6, pp. 3689 - 3700
We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover (X) over tilde -> X. The completion of this complex... 
Alexander polynomial | Periodic end | de Rham complex | MATHEMATICS | OPERATORS
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 10/2011, Volume 154, Issue 1, pp. 93 - 101
Journal Article
JOURNAL OF DIFFERENTIAL GEOMETRY, ISSN 0022-040X, 06/2011, Volume 88, Issue 2, pp. 333 - 377
We introduce a gauge-theoretic integer valued lift of the Rohlin invariant of a smooth 4-manifold X with the homology of S-1 x S-3. The invariant has two... 
CASSON INVARIANTS | MATHEMATICS | GAUGE-THEORY | BUNDLES | INDEX | HOMOLOGY | MODULI SPACES | EQUIVALENCE | SURFACES
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2010, Volume 248, Issue 1, pp. 139 - 154
In 1992, Xiao-Song Lin constructed an invariant h(K) of knots K subset of S-3 via a signed count of conjugacy classes of irreducible SU(2) representations of... 
Link group | Projective representation | Braid | MATHEMATICS | GAUGE-THEORY | braid | REPRESENTATION | link group | projective representation | HOMOLOGY
Journal Article
Topology and its Applications, ISSN 0166-8641, 2011, Volume 158, Issue 3, pp. 344 - 351
Let be a genus curve and a real structure with the maximal possible number of fixed circles. We study the real moduli space where is the induced real structure... 
Real moduli spaces | Stable holomorphic bundles | MATHEMATICS | MATHEMATICS, APPLIED | FLAT CONNECTIONS | COMPACT RIEMANN SURFACE | PERFECT MORSE FUNCTION
Journal Article
2002, Encyclopaedia of mathematical sciences, ISBN 9783540437963, Volume 1., xii, 223
Book
Pacific Journal of Mathematics, ISSN 0030-8730, 2002, Volume 205, Issue 2, pp. 465 - 490
Recent major progress in the study of the homology cobordism group of homology 3-spheres is related to the work of Fukumoto, Furuta, and Ue on their... 
SURGERY | MATHEMATICS | ORBIFOLDS
Journal Article
Geometry & Topology, ISSN 1465-3060, 10/2005, Volume 9, Issue 4, pp. 2079 - 2127
Journal Article
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