Geometry and Topology Seminar

This seminar discusses geometry and topology in a broad sense including (but not exclusively) Riemannian geometry, low dimensional topology and geometry, and geometric group theory.

Details

Rational formality and special holonomy

by Manuel Amann | University of Toronto
Time: 16:10  (Monday, Nov. 01, 2010)
Location: BA6180, Bahen Center, 40 St George St
Abstract:
Basically, due to a famous result of Berger the possible holonomy groups of (simply- connected) Riemannian manifolds are well-known. These special geometries—featuring prominent examples like Kahler manifolds or Joyce manifolds—often do possess remark- able topological properties. In this talk I shall discuss one property which virtually all these manifolds might have in common and which stems from Rational Homotopy Theory—namely formality. This expresses the fact that rationally the homotopy theory of these spaces might be no more complicated than their cohomology theory. After providing necessary concepts and giving an overview of the subject, I shall present new results including the formality of Positive Quaternion Kahler Manifolds.

Dates in this series

· Monday, Mar. 08, 2010: The fundamental group of random 2-complexes (Matthew Kahle)
· Monday, Mar. 15, 2010: Three Dimensional Manifolds All of Whose Geodesics Are Closed (John Olsen)
· Monday, Mar. 22, 2010: Curves on surfaces with large topology (Hugo Parlier)
· Friday, Mar. 26, 2010: New invariants in singularity theory (Rustam Sadykov)
· Friday, Mar. 26, 2010: The hidden smoothness of the space of stable maps (Jonathan Wise)
· Monday, Apr. 05, 2010: Moduli spaces of conics in curves (Chris Judge)
· Monday, Sep. 20, 2010: Total Q-curvature for CR manifolds (Kengo Hirachi)
· Monday, Sep. 27, 2010: Group completions of moduli spaces (Rustam Sadykov)
· Tuesday, Oct. 12, 2010: Pontryagin invariants and integral formulas for Milnor's triple linking number (Herman Gluck)
· Monday, Oct. 18, 2010: Positively curved polar manifolds (Fuquan Fang)
· Monday, Nov. 01, 2010: Rational formality and special holonomy (Manuel Amann)
· Monday, Nov. 08, 2010: Isoperimetric Inequalities -- methods and applications (Emanuel Milman)
· Monday, Nov. 15, 2010: From the sandwich to the waist (Alfredo Hubard)
· Monday, Nov. 29, 2010: TBA (Keith Burns)
· Monday, Nov. 29, 2010: Conjugate points and non-injectivity of the exponential map (Keith Burns)
· Monday, Jan. 17, 2011: Loop products and resonance for loop homology on spheres (Nancy Hingston)
· Monday, Jan. 31, 2011: A Variational Characterization of the Catenoid (Jacob Bernstein)
· Monday, Apr. 18, 2011: On the structure of conformally covariant powers of the Laplacian (Andreas Juhl)
· Monday, May. 09, 2011: Causality, Low conjecture and globally hyperbolic spacetimes (Vladimir Chernov)
· Monday, Sep. 26, 2011: Mapping degrees of self-maps of simply-connected manifolds (Manuel Amann)
· Monday, Oct. 17, 2011: Formality of Positive Quaternion Kähler manifolds (Vitali Kapovitch)
· Friday, Oct. 21, 2011: Kahler-Einstein metrics singular along a divisor (Yanir Rubinstein)
· Monday, Oct. 24, 2011: Diastolic inequality on a 2-sphere (Yevgeny Liokumovich)
· Monday, Nov. 14, 2011: TBA (Ian Hambleton)
· Monday, Nov. 14, 2011: Coarse geometry and group actions (Ian Hambleton)
· Monday, Nov. 21, 2011: Fundamental groups of manifolds with lower Ricci curvature bounds (Vitali Kapovitch)
· Monday, Nov. 28, 2011: Fundamental groups of manifolds with lower Ricci curvature bounds II (Vitali Kapovitch)
· Tuesday, Nov. 29, 2011: Asymptotic geometry, finite generation of fundamental groups, and harmonic functions (Bruce Kleiner)
· Friday, Dec. 09, 2011: Topological Complexity and H-Spaces (Gregory Lupton)
· Tuesday, Jan. 24, 2012: A new construction of compact $G_2$ manifolds by glueing families of Eguchi-Hanson spaces (Spiro Karigiannis)
· Thursday, Jan. 26, 2012: Coarse Differentiation and the rank of Teichmüller space (Kasra Rafi)
· Thursday, Feb. 16, 2012: Manifolds and spaces with Ricci curvature bounds (Toby Colding)
· Monday, Feb. 27, 2012: Homological and homotopical filling functions (Robert Young)
· Monday, Mar. 12, 2012: Algorithmic decidability of Thurston equivalence and geometrization of branched coverings (Michael Yampolsky)
· Monday, Mar. 26, 2012: On some problems in the geometry of surfaces in normed spaces (Dmitri Burago)
· Monday, Apr. 02, 2012: CANCELLED -- Scattering rigidity with trapped geodesics; the two dimensional case (Chris Croke)
· Monday, Sep. 10, 2012: Realisation and dismantlability (Piotr Przytycki)
· Friday, Oct. 05, 2012: The metric completion of Outer Space (Yael Algom Kfir)
· Monday, Oct. 15, 2012: Complexes which require large filling distortion in Euclidean space (Dominic Dotterrer)
· Tuesday, Nov. 06, 2012: A theorem of existence for Asymptotically Conical Calabi-Yau manifolds (Ronan Conlon)
· Monday, Nov. 19, 2012: Ricci Solitons of Cohomogeneity One (McKenzie Wang)
· Monday, Nov. 26, 2012: Complete affine 3-manifolds, Lorentzian and hyperbolic geometry (Bill Goldman)
· Monday, Dec. 03, 2012: Hyperbolic Group Boundaries and Cannon-Thurston Maps (Owen Baker)