The Kreck monoids l2q+1(ℤ[π]) detect s-cobordisms amongst certain bordisms between stably diffeomorphic 2q-dimensional manifolds and generalise the Wall surgery obstruction groups, . In this paper we identify as edge set of a directed graph with vertices equivalence classes quadratic forms on finitely generated free ℤ[π] modules. Our main theorem computes edges l2q+1(υ, υ′) ⊂ υ υ′ via an exact sequence

Abstract For every $k \geq 2$ and $n , we construct n pairwise homotopically inequivalent simply connected, closed $4k$ -dimensional manifolds, all of which are stably diffeomorphic to one another. Each these manifolds has hyperbolic intersection form is parallelisable. In dimension four, exhibit an analogous phenomenon for spin $^{c}$ structures on $S^2 \times S^2$ . $m\geq 1$ also provide similar $(4m-1)$ -connected $8m$ examples, where the number homotopy types in a stable diffeomorphism...

Abstract Assessing the disruptive nature of a line research is new area academic evaluation that moves beyond standard citation-based metrics by taking into account broader citation context publications or patents. The “CD index” and number related indicators have been proposed in order to characterize disruptiveness scientific This has generated lot attention recent years, yet there no general consensus on significance reliability disruption indices. More experimentation would be desirable,...

For every $k \geq 2$ we construct infinitely many $4k$-dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these has hyperbolic intersection form and is parallelisable. In fact such infinite sets. To achieve this prove a realisation result for appropriate subsets Kreck's modified surgery monoid $\ell_{2q+1}(\mathbb{Z}[\pi])$, analogous to Wall's the odd-dimensional obstruction $L$-group $L_{2q+1}^s(\mathbb{Z}[\pi])$.

Evaluating the disruptive nature of academic ideas is a new area research evaluation that moves beyond standard citation-based metrics by taking into account broader citation context publications or patents. The "$CD$ index" and number related indicators have been proposed in order to characterise mathematically disruptiveness scientific This has generated lot attention recent years, yet there no general consensus on significance reliability disruption indices. More experimentation would be...

Even-dimensional l -monoids and L-theory JÖRG SIXTSurgery theory provides a method to classify n-dimensional manifolds up diffeomorphism given their homotopy types n 5.In Kreck's modified version, it suffices know the normal type of 2 -skeletons.While obstructions in original live Wall's L-groups, are elements certain monoids .ZOE /.Unlike Kreck not well-understood.We present three help analyze  2k .ƒ/for ring ƒ.Firstly, if .ƒ/ is elementary (ie trivial), flip-isomorphisms must exist.In...

The monoids l_{2q+1}(Z[π]) detect s-cobordisms amongst certain bordisms between stably diffeomorphic 2q-dimensional manifolds and generalise the Wall simple surgery obstruction groups, L_{2q+1}^s(Z[π]) \subset l_{2q+1}(Z[π]). In this paper we give exact sequences which completely describe as a set use to compute its Grothendieck group. As consequence deduce cancellation results for with polycyclic-by-finite fundamental

In the 1980s Matthias Kreck developed a modified surgery theory with obstructions in hardly understood monoid $l_n(Z[π])$. This paper presents couple of purely algebraic tools to find out whether an element $l_{2q}(R)$ is "elementary" i.e. problem leads $h$-cobordism or not.

For every $k \geq 2$ and $n we construct $n$ pairwise homotopically inequivalent simply-connected, closed $4k$-dimensional manifolds, all of which are stably diffeomorphic to one another. Each these manifolds has hyperbolic intersection form is parallelisable. In dimension $4$, exhibit an analogous phenomenon for spin$^{c}$ structures on $S^2 \times S^2$. $m\geq 1$, also provide similar $(4m{-}1)$-connected $8m$-dimensional examples, where the number homotopy types in a stable diffeomorphism...