Let X be an arbitrary topological space and let Y be a closed connected oriented n-dimensional manifold.

Surface functionalization of liposomes can play a key role in overcoming the current limitations of nanocarriers to treat solid tumors, i.e., biological barriers and physiological factors. The phospholipid vesicles (liposomes) containing anticancer agents produce fewer side effects than non-liposomal anticancer formulations, and can effectively target the solid tumors. This article reviews information about the strategies for targeting of liposomes to solid tumors along with the possible targets in cancer cells, i.e., extracellular and intracellular targets and targets in tumor microenvironment or vasculature. Targeting ligands for functionalization of liposomes with relevant surface engineering techniques have been described. Stimuli strategies for enhanced delivery of anticancer agents at requisite location using stimuli-responsive functionalized liposomes have been discussed. Recent approaches for enhanced delivery of anticancer agents at tumor site with relevant surface functionalization techniques have been reviewed. Finally, current challenges of functionalized liposomes and future perspective of smart functionalized liposomes have been discussed.

Let f : M → N be a continuous map between two closed n-manifolds such that f * : H * (M, Z 2) → H * (N, Z 2) is an isomorphism. Suppose that M immerses in R n+k for 5 n < 2k. Then N also immerses in R n+k. We use techniques of normal bordism theory to prove this result and we show that for a large family of spaces we can replace the homology condition by the corresponding one in homotopy.

The purpose of this work is to classify, for given integers m, n ≥ 1, the bordism class of a closed smooth m-manifold X m with a free smooth involution τ with respect to the validity of the Borsuk-Ulam property that for every continuous map ϕ : X m → R n there exists a point x ∈ X m such that ϕ(x) = ϕ(τ (x)). We will classify a given free Z 2 -bordism class α according to the three possible cases that (a) all representatives (X m , τ ) of α satisfy the Borsuk-Ulam property; (b) there are representatives (X m 1 , τ 1 ) and (X m 2 , τ 2 ) of α such that (X m 1 , τ 1 ) satisfies the Borsuk-Ulam property but (X m 2 , τ 2 ) does not; (c) no representative (X m , τ ) of α satisfies the Borsuk-Ulam property.2010 Mathematics Subject Classification. Primary 55M20; Secondary 57R85, 57R75, 55M35.

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