Automorphisms of circle bundles over surfaces

1975 ◽  
pp. 212-214
Author(s):  
Michael H. Freedman
Keyword(s):  
Circle Bundles

scholarly journals Klein bottles in circle bundles

1971 ◽  
Vol 28 (2) ◽  
pp. 607-607
Author(s):  
John W. Wood
Keyword(s):  
Circle Bundles

scholarly journals Maximal tori in the contactomorphism groups of circle bundles over Hirzebruch surfaces

2003 ◽  
Vol 10 (1) ◽  
pp. 133-144 ◽  
Author(s):  
Eugene Lerman
Keyword(s):  
Circle Bundles ◽  
Maximal Tori ◽  
Hirzebruch Surfaces

scholarly journals Riemannian metrics on principal circle bundles over locally symmetric Kählerian manifolds

1982 ◽  
Vol 5 (1) ◽  
pp. 111-121 ◽  
Author(s):  
Yoshiyuki Watanabe
Keyword(s):  
Riemannian Metrics ◽  
Circle Bundles ◽  
Kählerian Manifolds

scholarly journals Tangent circle bundles admit positive open book decompositions along arbitrary links

Topology ◽  
2004 ◽  
Vol 43 (1) ◽  
pp. 215-232 ◽  
Author(s):  
Masaharu Ishikawa
Keyword(s):  
Open Book ◽  
Tangent Circle ◽  
Open Book Decompositions ◽  
Circle Bundles

scholarly journals Nonnegatively and positively curved invariant metrics on circle bundles

2005 ◽  
Vol 133 (8) ◽  
pp. 2449-2459 ◽  
Author(s):  
Krishnan Shankar ◽  
Kristopher Tapp ◽  
Wilderich Tuschmann
Keyword(s):  
Invariant Metrics ◽  
Circle Bundles ◽  
Positively Curved

scholarly journals CONFORMAL COURANT ALGEBROIDS AND ORIENTIFOLD T-DUALITY

2012 ◽  
Vol 10 (02) ◽  
pp. 1250084 ◽  
Author(s):  
DAVID BARAGLIA
Keyword(s):  
Line Bundle ◽  
Bilinear Form ◽  
Conformal Structure ◽  
Crossed Module ◽  
Courant Algebroids ◽  
Courant Algebroid ◽  
Circle Bundles ◽  
Twisted Cohomology ◽  
Free Involution ◽  
Special Case

We introduce conformal Courant algebroids, a mild generalization of Courant algebroids in which only a conformal structure rather than a bilinear form is assumed. We introduce exact conformal Courant algebroids and show they are classified by pairs (L, H) with L a flat line bundle and H ∈ H3(M, L) a degree 3 class with coefficients in L. As a special case gerbes for the crossed module (U(1) → ℤ2) can be used to twist TM ⊕ T*M into a conformal Courant algebroid. In the exact case there is a twisted cohomology which is 4-periodic if L2 = 1. The structure of Conformal Courant algebroids on circle bundles leads us to construct a T-duality for orientifolds with free involution. This incarnation of T-duality yields an isomorphism of 4-periodic twisted cohomology. We conjecture that the isomorphism extends to an isomorphism in twisted KR-theory and give some calculations to support this claim.

scholarly journals Invariants of Legendrian Knots in Circle Bundles

2003 ◽  
Vol 05 (04) ◽  
pp. 569-627 ◽  
Author(s):  
Joshua M. Sabloff
Keyword(s):  
Contact Structure ◽  
Homology Class ◽  
Graded Algebra ◽  
Legendrian Knots ◽  
Contact Homology ◽  
Circle Bundle ◽  
Differential Graded Algebra ◽  
Circle Bundles ◽  
Standard Contact ◽  
Definition Of

Let M be a circle bundle over a Riemann surface that supports a contact structure transverse to the fibers. This paper presents a combinatorial definition of a differential graded algebra (DGA) that is an invariant of Legendrian knots in M. The invariant generalizes Chekanov's combinatorial DGA invariant of Legendrian knots in the standard contact 3-space using ideas from Eliashberg, Givental, and Hofer's contact homology. The main difficulty lies in dealing with what are ostensibly 1-parameter families of generators for the DGA; these are solved using "Morse–Bott" techniques. As an application, the invariant is used to distinguish two Legendrian knots that are smoothly isotopic, realize a nontrivial homology class, but are not Legendrian isotopic.

scholarly journals EXPLICIT HORIZONTAL OPEN BOOKS ON SOME PLUMBINGS

2006 ◽  
Vol 17 (09) ◽  
pp. 1013-1031 ◽  
Author(s):  
TOLGA ETGÜ ◽  
BURAK OZBAGCI
Keyword(s):  
Contact Structure ◽  
Complex Surface ◽  
Contact Structures ◽  
Open Book ◽  
Open Books ◽  
Tight Contact ◽  
Weinstein Conjecture ◽  
Circle Bundles ◽  
Surface Singularities

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, on some Seifert fibered 3-manifolds we describe open books which are horizontal with respect to their plumbing description. As another application we describe horizontal open books isomorphic to Milnor open books for some complex surface singularities. Moreover we give examples of tight contact 3-manifolds supported by planar open books. As a consequence, the Weinstein conjecture holds for these tight contact structures [1].

scholarly journals Topological T-duality for general circle bundles

2014 ◽  
Vol 10 (3) ◽  
pp. 367-438 ◽  
Author(s):  
David Baraglia
Keyword(s):  
Circle Bundles

scholarly journals Normal circle bundles of complex hypersurfaces

1968 ◽  
Vol 20 (1) ◽  
pp. 29-53 ◽  
Author(s):  
Kentaro Yano ◽  
Shigeru Ishihara
Keyword(s):  
Circle Bundles
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