Motivated by Akbulut-Larson's construction of Brieskorn spheres bounding rational homology 4-balls, we explore plumbed 3-manifolds that bound circles and use them to construct infinite families 3-spheres 4-balls. Some these are new examples integer but do not In particular, find torus bundles over the circle circles, provide a simple method for constructing more general show that, example, $-1$...

We extend Lawrence's representations of the braid groups to relative homology modules, and we show that they are free modules over a Laurent polynomials ring. define homological operators actually provide representation for an integral version $U_q \mathfrak{sl}(2)$. suggest isomorphism between given basis standard tensor products Verma it preserve ring coefficients, action \mathfrak{sl}(2)$, g...

This work concerns finite free complexes with length homology over a commutative noetherian local ring $R$. The focus is on that have $\mathrm{dim}\, R$, which the smallest possible value, and in particular resolutions of modules projective dimension. Lower bounds are obtained Euler characteristic such short when $R$ strict complete intersection, also Dutta multiplicity, localization at its max...

1. TJ'he first step toward connecting these two basic concepts of topology was taken by L. E. J. Brouwer in 1912 by demonstrating that two continuous mappings of a two-dimensional sphere into itself can be continuously deformed into each other if and only if they have the same degree (that is, if they are equivalent from the point of view of homology theory). After having generalized Brouwer's ...