The Witt group of real surfaces

2020 ◽  
pp. 157-193
Author(s):  
Max Karoubi ◽  
Charles Weibel
Keyword(s):  
Witt Group

Witt group

2017 ◽  
pp. 163-174
Author(s):  
Kazimierz Szymiczek
Keyword(s):  
Witt Group

The Witt group of a smooth complex surface

1987 ◽  
Vol 277 (3) ◽  
pp. 469-481 ◽  
Author(s):  
Fernando Fern�ndez-Carmena
Keyword(s):  
Complex Surface ◽  
Witt Group ◽  
Smooth Complex

Discriminants of Casson–Gordon invariants

1992 ◽  
Vol 112 (1) ◽  
pp. 127-139 ◽  
Author(s):  
Patrick Gilmer ◽  
Charles Livingston
Keyword(s):  
Witt Group ◽  
Root Of Unity ◽  
Wide Range ◽  
Genus Two

Casson–Gordon invariants were first used to prove that certain algebraically slice knots in S3 are not slice knots [2, 3]. Since then they have been applied to a wide range of problems, including embedding problems and questions relating to boundary links [2, 10, 21, 25]. The most general Casson–Gordon invariant takes its value in L0(ℚ(ζd)(t)) ⊗ ℚ; here ζd denotes a primitive dth root of unity. Litherland [20] observed that one could usually tensor with ℤ(2) instead of ℚ, and in this way preserve the 2-torsion in the Witt group. He then constructed new examples of non-slice genus two knots which were detected with torsion classes in L0(ℚ(ζd)) ⊗ ℤ(2) modulo the image of L0(ℚ(ζd)) ⊗ ℤ(2).

scholarly journals The graded Witt group kernel of biquadratic extensions in characteristic two

2012 ◽  
Vol 370 ◽  
pp. 297-319 ◽  
Author(s):  
Roberto Aravire ◽  
Bill Jacob
Keyword(s):  
Witt Group ◽  
Characteristic Two

scholarly journals Symplectic bilinear forms on affine real algebraic surfaces

1989 ◽  
Vol 31 (2) ◽  
pp. 195-198
Author(s):  
W. Kucharz
Keyword(s):  
Commutative Ring ◽  
Algebraic Surfaces ◽  
Bilinear Forms ◽  
Witt Group ◽  
Real Algebraic Surfaces ◽  
Definition Of

Given a commutative ring A with identity, let W–1(A) denote the Witt group of skew-symmetric bilinear forms over A (cf. [1] or [7] for the definition of W–1 (A)).

scholarly journals Symplectic complex bundles over real algebraic four-folds

1989 ◽  
Vol 47 (3) ◽  
pp. 430-437
Author(s):  
Wojciech Kucharz
Keyword(s):  
Algebraic Variety ◽  
Real Algebraic Variety ◽  
Bilinear Forms ◽  
Cohomology Groups ◽  
Witt Group ◽  
Regular Functions

AbstractLetXbe a compact affine real algebraic variety of dimension 4. We compute the Witt group of symplectic bilinear forms over the ring of regular functions fromXto C. The Witt group is expressed in terms of some subgroups of the cohomology groups.

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