arXiv subjects

V Uma

Publications and source records attributed to V Uma.

2 recordsLinked to original sources

arXiv2017

Results on the topology of generalized real Bott manifolds

Generalized Bott manifolds (over $\mathbb C$ and $\mathbb R$) have been defined by Choi, Masuda and Suh. In this article we extend the results of arXiv:1609.05630 on the topology of real Bott manifolds to generalized real Bott manifolds. We give a presentation of the fundamental group, prove that it is solvable and give a characterization for it to be abelian. We further prove that these manifolds are aspherical only in the case of real Bott manifolds and compute the higher homotopy groups. Furthermore, using the presentation of the cohomology ring with $\mathbb Z_2$-coefficients, we derive a combinatorial characterization for orientablity and spin structure.

math.AT↗

arXiv2006

On the fundamental group of real toric varieties

Let $X(Δ)$ be the real toric variety associated to a smooth fan $Δ$. The main purpose of this article is: (i) to determine the fundamental group and the universal cover of $X(Δ)$, (ii) to give necessary and sufficient conditions on $Δ$ under which $π_1(X(Δ))$ is abelian, (iii) to give necessary and sufficient conditions on $Δ$ under which $X(Δ)$ is aspherical, and when $Δ$ is complete, (iv) to give necessary and sufficient conditions for $\cc_Δ$ to be a $K(π,1)$ space where $\cc_Δ$ is the complement of a real subspace arrangement associated to $Δ$.

math.AG↗