Remark on the Poincaré duality theorem

Remark on Poincaré duality for SU q ( 2 ) Partha

Let A be the C∗-algebra associated with SUq(2), J be the modular conjugation coming from the Haar state and let D be the generic equivariant Dirac operator for SUq(2). We prove in this article that there is no element in JAJ , other than the scalars, that have bounded commutator with D. This shows in particular that JAJ does not contain any Poincaré dual for SUq(2). AMS Subject Classification N...

POINCARÉ DUALITY COMPLEXES IN DIMENSION FOUR 3 Theorem 5

We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of PD–complexes. Generalizing Turaev’s fundamental triples of PD–complexes we introduce fundamental triples for PDn–complexes and show that two PDn–complexes are orientedly homotopy equivalent if and only if their fundamental triples are isomorphic. As applications we establish a conjec...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

A Remark on Zoloterav’s Theorem

Let n ≥ 3 be an odd integer. For any integer a prime to n, define the permutation γ a,n of {1,. .. , (n − 1)/2} by γ a,n (x) = n − {ax} n if {ax} n ≥ (n + 1)/2, {ax} n if {ax} n ≤ (n − 1)/2, where {x} n denotes the least nonnegative residue of x modulo n. In this note, we show that the sign of γ a,n coincides with the Jacobi symbol a n if n ≡ 1 (mod 4), and 1 if n ≡ 3 (mod 4).

Remark on Poincaré duality for SUq(2)

Let A be the C∗-algebra associated with SUq(2), J be the modular conjugation coming from the Haar state and let D be the generic equivariant Dirac operator for SUq(2). We prove in this article that there is no element in JAJ , other than the scalars, that have bounded commutator with D. This shows in particular that JAJ does not contain any Poincaré dual for SUq(2). AMS Subject Classification N...